Research paper archive
October 2026
72 papers
Selected in October 2026
Quantum information · Theory
Sharp Tilting Inequalities
arXiv:2610.39598v1 ↗PDF ↗Submitted 29 October 2026
- Question
- Error-exponent arguments often bound a ratio like \(x/(1+x)\) by a power of \(x\), which turns a success probability into a Rényi-type quantity. For matrices, the ratio becomes a derivative of the logarithm of a noncommuting sum. What is the best constant in the resulting trace inequality, and does it match the scalar one?
- Result
- For positive semidefinite \(A,B\) and \(\alpha\in[1/2,1]\) with \(s=(1-\alpha)/\alpha\), \[\mathrm{Tr}\big[A\,D\log[A^\alpha+B^\alpha](B^\alpha)\big]\le s^s(1-s)^{1-s}\,\mathrm{Tr}[A^\alpha B^{1-\alpha}].\] The coefficient is optimal and equals the scalar one, with equality in the interior exactly when \(B^\alpha=\frac{1-s}sA^\alpha\). The same bound holds for the symmetric quotient, and both extend to trace-class \(A\) and unbounded \(B\).
Methods Lifting a scalar inequality through a one-parameter superoperator; Proving a trace bound by shifting and monotonicity
Read the full entry →Quantum computing · Theory
Quantum Query Complexity of Tournament Solutions
arXiv:2610.39702v1 ↗PDF ↗Submitted 29 October 2026
- Question
- Given the outcomes of pairwise comparisons among \(N\) alternatives, a tournament solution names the winners. Classically, nearly every standard solution needs \(\Theta(N^2)\) comparisons, so they cannot be told apart by cost. How many queries do they need when comparisons can be made in superposition, and does the classical uniformity survive?
- Result
- It does not. The top cycle takes \(\tilde\Theta(N)\) queries, a Condorcet winner takes \(\tilde\Theta(\sqrt N)\), and a strong king takes \(\Theta(N^{3/2})\). The whole Copeland set needs \(\Theta(N^2)\), so reading every comparison is optimal up to a constant, while a single Copeland winner needs only \(\Theta(N^{3/2})\). The uncovered set lies between \(\Omega(N^{3/2})\) and \(O(N^2)\).
Methods Ambainis's adversary with single-flip relations on rows of fixed weight; Turning the top cycle into interval covering along a Hamiltonian path
Read the full entry →Foundations of quantum mechanics · Theory
Three-dimensional QCA that are not stably circuits
arXiv:2610.40235v1 ↗PDF ↗Submitted 29 October 2026
- Question
- Quantum cellular automata are locality-preserving automorphisms of an operator algebra, and the trivial ones are finite-depth circuits and translations. In three dimensions, explicit Clifford examples were known not to be Clifford circuits, but none had been shown unconditionally to be nontrivial against arbitrary circuits. Are any of them genuinely new, even with ancillas allowed?
- Result
- For every odd prime \(p\), the chiral \(\mathbb Z_p\) Clifford QCA are not finite-depth circuits, even after adding arbitrary ancillas and composing with translations. The proof uses a new invariant \(I\) of two-dimensional invertible subalgebras, valued in positive rationals modulo squares, which takes the value \([p]\) on these examples. The group of three-dimensional QCA modulo stabilized circuits and translations is not finitely generated.
Methods An index defined up to squares by truncating an involution; Reading the index from a determinant over Laurent polynomials
Read the full entry →Quantum computing · Theory
Rapid mixing for Gibbs samplers for quantum spin systems with all-to-all interactions
arXiv:2610.40361v1 ↗PDF ↗Submitted 29 October 2026
- Question
- A Lindbladian can keep a Gibbs state stationary and still approach it too slowly to be useful. Earlier logarithmic mixing proofs at high temperature depended on geometry or on bounds for the growth of the interaction graph, which degrade badly on dense graphs. How much of that dependence is necessary for two-body qubit Hamiltonians?
- Result
- None of the graph growth is needed. If \(\beta\Lambda<1/100\), where \(\Lambda\) is the largest total interaction strength at any qubit, the KMS-balanced sampler of Bakshi, Liu, Moitra and Tang reaches trace-norm error \(\varepsilon\) from any initial state by time \(\frac13\log(2n/\varepsilon)\). On the complete graph with couplings scaled by \(1/\sqrt{n-1}\), the allowed \(\beta\) scales as \(n^{-1/2}/J\), against \(n^{-5/2}/J\) from the earlier theorem.
Methods Summing connected commutators by interaction weight; From a Dobrushin contraction to a logarithmic mixing time
Read the full entry →Foundations of quantum mechanics · Theory
On the Quantum Chromatic Gap II
arXiv:2610.40571v1 ↗PDF ↗Submitted 29 October 2026
- Question
- Two separated players can use entanglement to win the graph colouring game with fewer colours than the graph's chromatic number. Since 1999 the largest known separation had the classical chromatic number exponential in the quantum one. Is the classical number bounded by any function of the quantum number, so that enough extra colours would always replace entanglement?
- Result
- No. For every \(c\) there is a graph with quantum chromatic number 3 and classical chromatic number above \(c\). The route is a proof, for every \(d\ge4\), of a conjecture of Ciardo: there are \(d\)-to-1 games of arbitrarily small classical value with perfect finite-dimensional quantum strategies whose measurements commute on arbitrarily large neighbourhoods.
Methods Stretching a contextuality proof with wires of trivial equations; Parallel repetition with a tensor-power strategy
Read the full entry →Quantum information · Theory
Optimal Diamond Distance Estimation for Unitary Channels
arXiv:2610.40623v1 ↗PDF ↗Submitted 29 October 2026
- Question
- The diamond distance between two channels sets the best single-use probability of distinguishing them, and it is the usual measure of implementation error. Given only black-box access to \(d\)-dimensional unitaries \(U\) and \(V\) and their inverses, how many queries are needed to estimate it to additive error \(\varepsilon\)? The known bounds were \(O(d\log^2d/\varepsilon)\) and \(\Omega(\sqrt d/\varepsilon)\).
- Result
- \(O(\sqrt d/\varepsilon)\) queries suffice, with success probability at least \(2/3\). This matches the lower bound of Jeon and Oh for certification, so the query complexity is settled up to a constant. The algorithm needs no controlled access to \(U\) or \(V\) and no assumption on where the spectrum lies.
Methods Relative phases without controlled access; Using the flatness of the distance near its maximum
Read the full entry →Quantum computing · Theory with formal verification
Optimal Linear Combination of Hamiltonian Simulation for Dissipative Dynamics
arXiv:2610.39541v1 ↗PDF ↗Submitted 29 October 2026
- Question
- Linear combination of Hamiltonian simulation (LCHS) writes \(\mathrm e^{-tA}\) with \(A=X+\mathrm iY\) and \(X\succeq0\) as an integral of unitary evolutions, weighted by a kernel. The cost is governed by the kernel’s window \(R\) and total variation \(\lambda\). Ni and Ying’s kernel achieves \(\lambda R\sim\frac{2\mathrm e}{\pi}\ln\frac1\epsilon\), but only upper bounds were known. Can any kernel do better in the worst case?
- Result
- No. For every budget, \(\min_\mu\mathcal E(\mu)=1-\lambda\) if \(\lambda\le p\), and \(q(p/\lambda)^{p/q}\) if \(\lambda\ge p\), where \(p=\frac2\pi\arctan R\) and \(q=1-p\). The minimum cost is \(J(\epsilon)=\frac{2\mathrm e}{\pi}(\ln\frac1\epsilon-\ln\ln\frac1\epsilon)+o(1)\). The Ni–Ying family is therefore optimal, and the value holds for time-dependent generators as well.
Methods A lower bound from harmonic measure and a dual function; Reducing the two-parameter budget to a one-variable optimum
Read the full entry →Foundations of quantum mechanics · Theory
Inevitability of the Petz transpose map
arXiv:2610.40158v1 ↗PDF ↗Submitted 29 October 2026
- Question
- Given a prior and a stochastic model, Bayes’ rule fixes the reverse conditional probabilities. A quantum state and a channel do not define a joint state as unambiguously, so several candidates for a quantum Bayes’ rule exist. Do consistency requirements on reversing a channel, with no appeal to a joint state or a figure of merit, single out one rule?
- Result
- For channels between finite-dimensional full matrix algebras, exactly one retrodiction assignment is involutive, respects sequential and parallel composition, and inverts unitaries: the Petz map \(\mathcal R_{\pi\to\sigma}[\Phi](X)=\sqrt\pi\,\Phi^\dagger(\sigma^{-1/2}X\sigma^{-1/2})\sqrt\pi\). Dropping involutivity leaves a family of doubly rotated Petz maps, and adding continuity in the prior reduces it to the one-parameter rotated Petz maps.
Methods Building a mixture from circuits to force affinity; Quantum Bayes update for measurement outcomes
Read the full entry →Quantum computing · Experiment
High-Fidelity Universal Quantum Gates in a Cryogenic Atom Array
arXiv:2610.40329v1 ↗PDF ↗Submitted 29 October 2026
- Question
- Rydberg gates in neutral-atom arrays are approaching the limit set by Rydberg decay, most of which at room temperature comes from blackbody-driven transitions that also create contaminant states and correlated errors. A cryostat suppresses these transitions, but restricted optical access and field control have kept universal high-fidelity gates out of cryogenic arrays. Can such gates be done there at state-of-the-art fidelity?
- Result
- In a \(^{133}\)Cs array inside 4 K shields, the authors measure a single-qubit Clifford fidelity of 99.970(2)% and a raw CZ fidelity of 99.76(8)% by echo randomised benchmarking, with 99.78(10)% by symmetric stabilizer benchmarking. The gate lasts 316 ns at \(\Omega=2\pi\times4.3\) MHz, using direct single-photon excitation at 319 nm to a \(55P_{3/2}\) Rydberg state. A simulated error budget predicts 99.80%, with Rydberg decay contributing only \(2.7\times10^{-4}\) and Doppler shifts \(1.26\times10^{-3}\).
Methods An error budget that names the next improvement; Choosing geometry to exploit an anisotropic interaction
Read the full entry →Quantum information · Theory
Quantum communication: a discrimination approach
arXiv:2610.40358v1 ↗PDF ↗Submitted 29 October 2026
- Question
- The two familiar routes to quantum capacity are packing, where Bob distinguishes outputs, and decoupling, where the reference becomes independent of the environment. Decoupling often proves only that a decoder exists. Can entanglement generation be analysed directly as a state-discrimination problem, with an explicit decoder and bounds valid at every block length?
- Result
- For any input and \(\alpha\in[1/2,1)\), random codes built from the source satisfy \(\overline\varepsilon_{\rm EG}(d)\le c_\alpha2^{-\frac{1-\alpha}\alpha(I_\alpha(R\rangle B)_\rho-\log_2d)}\), with decoders derived from Petz recovery (or averaged rotated Petz recovery), where \(I_\alpha\) is the Petz–Rényi coherent information. The coefficient \(c_\alpha\) is sharp. For product sources this gives exponential error decay at every rate below the coherent information, with an explicit exponent.
Methods Weyl covariance turns a decoder into a measurement and back; A sharp tilting inequality tested by the identity channel
Read the full entry →Foundations of quantum mechanics · Theory
What Can Be Computed with Indefinite Causal Structure?
arXiv:2610.40573v1 ↗PDF ↗Submitted 29 October 2026
- Question
- A quantum circuit, even in superposition, still has a causal order between its gates. Process matrices keep ordinary quantum mechanics locally and drop the global order. Earlier work placed polynomial-time process matrix computation between BQP and PP and left open whether it exceeds BQP. Does it, and does it still do so when the process is required to be unitary at every level?
- Result
- Process matrix computation solves every problem in NP in polynomial time, using purifiable processes whose generated channels are unitary but whose generating circuits are not. Requiring pure processes, the paper gives explicit unitary generators that solve unique-sink orientation (USO) with one use of the generated channel and probability 1. If USO has no quantum polynomial-time algorithm, pure indefinite causal order goes beyond BQP within the formalism.
Methods Closing a loop to post-select a teleportation outcome, with a valid channel; Row orthogonality from a coordinate that is flipped equally
Read the full entry →Quantum information · Theory with formal verification
Classical communication over quantum channels: does entanglement help in nature?
arXiv:2610.40585v1 ↗PDF ↗Submitted 29 October 2026
- Question
- Can entangling codewords across channel uses raise the classical communication rate? Hastings showed that it sometimes can, so \(\mathcal C(\mathcal A)>\chi_{\max}(\mathcal A)\) for some channels, but the known examples have enormous dimension. Which physically natural channels genuinely have no advantage, in any dimension?
- Result
- A new Schur-weighted block entropy inequality implies strong Holevo additivity, \(\chi_{\max}(\mathcal A\otimes\mathcal M)=\chi_{\max}(\mathcal A)+\chi_{\max}(\mathcal M)\) for every partner \(\mathcal M\), for all phase-covariant channels in any dimension, including multi-level amplitude damping, generalized dephasing and damping-dephasing channels. It also recovers additivity for all qubit-to-qubit channels. For these channels, \(\mathcal C=\chi_{\max}\), so the single-letter Holevo information is the classical capacity.
Methods Rank-one reduction by operator monotonicity; A weaker additivity criterion using the optimal output centre
Read the full entry →Quantum computing · Theory
Quantum State Preparation for Complex-Valued Amplitudes
arXiv:2610.36680v1 ↗PDF ↗Submitted 27 October 2026
- Question
- Quantum algorithms often compute numbers into binary registers with reversible arithmetic, but then need those numbers as amplitudes. For a complex \(z=x+iy\), the usual route encodes \(x\) and \(y\) separately and adds them with a linear combination of unitaries, which fixes the normalisation by the ranges of \(x\) and \(y\). How can \(z/\alpha\) be loaded coherently, for inputs in superposition, with a normalisation set by \(|z|\) itself?
- Result
- The procedure computes the magnitude \(r'\) and argument \(\phi'\) of \(z\) reversibly with CORDIC, which uses only shifts and additions. It then encodes \(r'/\alpha\) with an exact binary-to-amplitude routine, applies one phase gate per bit of \(\phi'\) to obtain \(e^{i\phi'}\), and uncomputes the arithmetic. The cost is \(O(n^2)\) Toffoli and \(T\) gates and \(O(n)\) ancillas, with error \(|r'e^{i\phi'}-z|=O(2^{-(n-l)})\) for \(n\)-bit inputs with \(l\) integer bits. A reversible in-place multiplication by \(1+2^{-2j}\), exactly invertible despite rounding, lets each CORDIC step run without storing an extra copy of a coordinate.
Methods CORDIC: rotation by shifts and additions; Exact inversion of a rounded in-place product
Read the full entry →Foundations of quantum mechanics · Theory and numerical analysis
Qubit-environment entanglement in pure dephasing dynamics for mixed initial states
arXiv:2610.36936v1 ↗PDF ↗Submitted 27 October 2026
- Question
- When a qubit only dephases, the joint qubit–environment state for a pure initial qubit is separable exactly when the environment ends up in the same state whichever pointer state the qubit is in, \(\hat R_{00}(t)=\hat R_{11}(t)\). This test made it possible to tell decoherence by entanglement from decoherence by classical correlations, and even to detect the difference on the qubit alone. Real qubits are already partly mixed. Does the test survive, and does entanglement then evolve as it does for pure qubits?
- Result
- If \(\hat R_{00}(t)=\hat R_{11}(t)\), the joint state stays separable, and zero-discord, for any initial qubit coherence. Otherwise, the family of minors that gave the pure-state criterion becomes only a witness: a negative minor proves entanglement, but nonnegative minors prove nothing. A Schur complement reduces the exact partial-transpose test to a matrix \(\hat D\) of the environment’s dimension, whose diagonal entries are those minors. Mixed qubits show behaviour impossible for pure ones: a separable initial period followed by sudden birth of entanglement, death and rebirth, and no entanglement at all during an entangling evolution when the qubit is strongly mixed. In a model of an NV-centre spin with up to five nuclear spins, the minors miss entanglement, sometimes for the whole evolution.
Methods Schur-complement reduction of a partial-transpose test; Common eigenbasis as a certificate of classical dephasing
Read the full entry →Foundations of quantum mechanics · Theory and numerical analysis
Certification Time for Weak-Force-Mediated Entanglement between Levitated Particles
arXiv:2610.37094v1 ↗PDF ↗Submitted 27 October 2026
- Question
- Experiments with levitated nanoparticles aim to show that a weak force, and eventually gravity, entangles the motion of two particles. Producing the entangled state is only half the task: it has to be told apart from separable states using a finite number of noisy measurements, taken one run at a time. How many measurements, and how much laboratory time, does certification need, and which protocol reaches the weakest forces?
- Result
- For a two-mode Gaussian state with smallest partially transposed symplectic eigenvalue \(\tilde\nu_-<1\), certification at \(z\) standard deviations needs about \(N_\star=(z\alpha/(1-\tilde\nu_-))^2\) measurements. With isotropic readout noise \(\xi\), \(\alpha\ge\tilde\nu_-+\xi\), with equality for symmetric thermal two-mode squeezed states, while local squeezing leaves the entanglement unchanged and makes \(\alpha\) arbitrarily large. In release–recapture, at a fixed ratio of diffusion to coupling, the entanglement stays finite as the force weakens but \(N_\star\) grows as \(1/g\) and the total time as \(g^{-3/2}\). Release–recapture certifies entanglement at couplings orders of magnitude weaker than continuous monitoring, and the release time that certifies fastest is longer than the one that entangles most.
Methods Delta-method error bars for a covariance witness; Weak-coupling limit at a fixed noise-to-coupling ratio
Read the full entry →Quantum information · Theory
Matrix Samplers and Quantum-Proof Extractors: Their Correspondence and Almost-Optimal Constructions
arXiv:2610.37122v1 ↗PDF ↗Submitted 27 October 2026
- Question
- To estimate the average of a bounded \(D\times D\) matrix-valued function in operator norm, \(O(\varepsilon^{-2}\log(2D/\delta))\) independent samples suffice, but each costs \(m\) fresh random bits. Matrix samplers try to keep nearly that sample count while using only \(m+O(\log(D/\delta))\) random bits. Classically, Zuckerman showed that averaging samplers and randomness extractors are the same objects. What kind of extractor is a matrix sampler, and can the correspondence give better constructions?
- Result
- A matrix sampler for \(D\times D\) matrices is the same thing as a seeded extractor whose output stays uniform against an adversary holding about \(\log(2D)\) qubits of side information, up to factor-two losses in the error. The paper then builds an explicit strong quantum-proof extractor with seed \((1+\alpha)\log a+(2+\alpha)\log(1/\eta)+O_\alpha(1)\) and output \(n-O_\alpha(a+\log(1/\eta))\) for sources of conditional min-entropy \(n-a\). Through the correspondence, this gives explicit strong matrix samplers with \(m+O_\alpha(\log(D/\delta))\) random bits and \(O_\alpha(\varepsilon^{-2-\alpha}\log^{1+\alpha}(D/\delta))\) samples, replacing a polynomial dependence on \(D\) in earlier work by a logarithmic one. It also gives quantum-proof extractors with seed \(O(\log(n/\eta))\) and output \(\Omega(n)\) for every constant entropy rate, where earlier constructions needed rate above one half.
Methods Hermitian dilation turns a matrix deviation into a quantum distinguisher; Shortening a seed with 2ℓ-wise independent candidate seeds
Read the full entry →Quantum information · Theory and numerical analysis
Prepare-and-measure quantum key distribution from a bound on information leakage
arXiv:2610.37296v1 ↗PDF ↗Submitted 27 October 2026
- Question
- Every key distribution protocol has to limit what escapes the users’ laboratories. In a prepare-and-measure protocol this cannot be strict, since the source must send out a signal that depends on Alice’s private input. The minimal assumption is therefore a bound on how much the emitted systems, intended signal and side channels together, reveal about the input. Can that single number replace a model of the source’s states, dimension and energy, with nothing assumed about Bob’s measurement device?
- Result
- Yes, against collective attacks. The leakage bound states that the optimal number of correctly guessed inputs, out of \(n\) sent once each, is at most \(G\), with \(G=2\) meaning one bit. Statistics reproducible by a classical message within the same bound certify no key. This rules out all two-state protocols such as B92, and all matched-basis protocols such as BB84 and the six-state protocol. Tilting Bob’s measurements restores security: four qubit protocols certify one secret bit per key round in the ideal case, through a self-test on a virtual entanglement-based twin. With noise, the best tolerates visibility 0.838 (8.1% bit error rate) and the loss thresholds are \(\eta\ge0.764\), about 1.2 dB. Numerically, the rates match the device-independent rates of the entanglement-based twins.
Methods Leakage as an operator inequality, and a virtual entanglement-based protocol; Copy-the-message attacks on classical models with bounded information
Read the full entry →Quantum computing · Theory and numerical analysis
Meet-in-the-Middle Compilation of the [CNOT] Class with Fibonacci Anyons
arXiv:2610.37552v1 ↗PDF ↗Submitted 27 October 2026
- Question
- Two qubits encoded in six Fibonacci anyons live in a five-dimensional fusion space, one dimension more than two qubits need. The only exchange that entangles the qubits, \(\sigma_3\), is also the only one that couples them to the fifth, noncomputational state, so every entangling braid leaks. How small can the leakage of a braid equivalent to CNOT up to single-qubit gates be at a given length, and is exhaustive search better than random sampling?
- Result
- A GPU meet-in-the-middle search over all \(5^{21}\) positive words finds at length 21 a braid with leakage \(\ell=3.95\times10^{-3}\) and distance \(7.8\times10^{-9}\) to the CNOT class, less leakage than the best previously sampled braid of length 39. Restricting to \(\{\sigma_1,\sigma_2,\sigma_3\}\), to words starting and ending with \(\sigma_3\), to palindromes and to Garside normal forms extends exhaustive search to length 72; at length 69 it finds \(\ell=8.8\times10^{-11}\) with distance \(4.3\times10^{-10}\). The paper proves that leakage lies in \(\mathbb Z[\varphi]\) and that any nonzero leakage satisfies \(\ell\ge1/(1+C^{2L})\) with \(C\approx2.89\), and that for long random words the leakage distribution tends to \(\ell^{d-1}\).
Methods Galois-conjugate lower bound on an algebraic quantity; Haar limit of one matrix element and the cost of sampling
Read the full entry →Quantum computing · Theory and numerical analysis
Correlation-sensitive magic-state distillation from spin-squeezed neutral atoms
arXiv:2610.36963v1 ↗PDF ↗Submitted 27 October 2026
- Question
- Magic-state distillation is analysed for independent noisy inputs, with a fidelity threshold above which each round improves the resource. Neutral-atom factories prepare many resource blocks in parallel under shared interactions and control fields, which correlates their errors. Can such correlations defeat distillation even when every input is above threshold, and which measurable quantity decides?
- Result
- Yes. For the five-to-one Bravyi–Kitaev protocol with independent local Clifford twirls, the accepted output depends on the joint input only through sums \(A_k\) of \(k\)-body correlators along the target axis: \(p_{\rm acc}=(3+A_4)/48\) and \(t_{\rm out}=(A_3-2A_5)/(3+A_4)\). Distillation improves on the mean input exactly when \(G=A_3-2A_5-\bar t(3+A_4)>0\). Inputs with identical one- and two-qubit reduced states can have opposite gains, and in finite-range Ising simulations of a 25-atom source, interblock correlations reverse the gain while the product of the same local states gains.
Methods Stabilizer expansion of a code projection on correlated inputs; Symmetry selection under code projection
Read the full entry →Foundations of quantum mechanics · Experiment
Experimental evidence for quantum Brownian motion in electron-metal decoherence
arXiv:2610.37293v1 ↗PDF ↗Submitted 27 October 2026
- Question
- Twenty years ago Anglin, Paz and Zurek proposed that an electron passing close to a metal loses coherence through quantum Brownian motion: its image charge dissipates energy in the metal, and by the fluctuation–dissipation theorem the same process randomizes the electron’s phase. Interferometer experiments near silicon found decoherence two orders of magnitude below the prediction, and those near gold were at the edge of detectability. Can electron–metal decoherence be measured and compared quantitatively with the theory?
- Result
- Yes, using a diffractometer instead of an interferometer. Diffracted 1.67 keV electrons enter a gold-plated microchannel at milliradian grazing incidence and bounce off the wall at sub-nanometre distance, which raises the interaction strength \(\Delta t/y^3\) to about \(10^7\) ps/μm³. All diffraction orders broaden equally and fringe visibility falls to 30–60%. The measured decoherence rate peaks at 182 μm⁻² at a tilt of 4.6 mrad, close to the classical-trajectory prediction of 216 μm⁻², and a standing-wave model reproduces the turnover at small tilt with a fitted gold resistivity of \(37\pm5\) nΩ m.
Methods Integrating a local decoherence rate along a trajectory; Intra-beam coherence as a short-baseline decoherence detector
Read the full entry →Quantum information · Theory
Measurement incompatibility and noiseless quantum codes
arXiv:2610.37347v1 ↗PDF ↗Submitted 27 October 2026
- Question
- A quantum channel can destroy the incompatibility of measurements but never create it. Which channels preserve the incompatibility of every finite family of measurements? Chitambar and Zhang conjectured that, when the input is larger than the output, such a channel must carry a noiseless copy of its output space, and Uola and coauthors asked whether every dimension has a measurement family that is incompatible on the full space but compatible on every proper subspace.
- Result
- Both questions are settled. A channel from dimension \(D\) to \(d\) preserves all incompatibility if and only if an isometry \(W\) encodes every output state noiselessly, \(\mathcal N(W\rho W^\dagger)=\rho\). One explicit family of \(d^2\) binary measurements is a complete test: its compatibility threshold is \(s=1\), and any channel that keeps that threshold has such a code. The same family is incompatible on \(\mathbb C^d\) and compatible on every proper subspace, for every \(d\ge2\). If the threshold shifts by a small \(\delta\), an approximate encoding has diamond-norm error at most \(2c^2\delta^2\).
Methods Dual-frame expansion of a dilation defect; Rigid parents of rank-one measurements
Read the full entry →Quantum computing · Theory
Classical Verification of Quantum Computation Beyond the Polynomial Hierarchy
arXiv:2610.37635v1 ↗PDF ↗Submitted 27 October 2026
- Question
- Can a classical polynomial-time verifier be convinced of the outcome of a quantum computation by the efficient quantum computer that ran it, with no cryptographic assumption? This is open for all of BQP, and every quantum problem known to have such a proof system lies in AM or was excluded only from MA relative to an oracle. Does efficient classical verification force a problem into the polynomial hierarchy?
- Result
- Not by any relativizing argument. Relative to a classical oracle, a variant of recursive Fourier sampling is decided exactly in quantum polynomial time, lies outside the polynomial hierarchy, and has a public-coin interactive proof with a classical verifier, an efficient quantum honest prover, perfect completeness and soundness error \(1/4\) against unbounded provers, using at most \(\log n/4\) messages. The message count can be made to grow as slowly as any unbounded computable function, and for a suitable oracle it is optimal up to a constant factor.
Methods Recursive spot-checks with a height-independent soundness invariant; Switching under correlated projections via a rank bound
Read the full entry →Foundations of quantum mechanics · Theory and numerical analysis
Network nonlocality with tripartite entangled sources
arXiv:2610.35838v1 ↗PDF ↗Submitted 26 October 2026
- Question
- Network nonlocality has mostly been studied with sources that emit pairs of particles. A three-qubit source has two distinct notions of nonlocality: the Mermin inequality excludes fully local models, and the Svetlichny inequality certifies genuine tripartite nonlocality. When independent sources emit three-qubit states and central nodes measure without any input, how is a network violation related to these two single-source tests?
- Result
- It depends on the wiring. In the closed network, where two input-free central nodes each hold one particle from every source, Bell-state measurements give a two-copy value at least the normalized Svetlichny value, \(\mathcal N_{\rm c}\ge\mathcal S/4\); every entangled generalized GHZ state, and even some biseparable states, violate the network inequality. In the open network, with one central node, the value is at most the normalized Mermin value, \(\mathcal N_{\rm o}\le\mathcal M/2\). With \(n\) sources, the largest violation of these two-correlator inequalities is \(\sqrt2\) (closed) or \(2\) (open) for even \(n\), but only \(2^{1/2-1/(2n)}\) or \(2^{1-1/(2n)}\) for odd \(n\).
Methods Two perpendicular directions from one end node; Anticommutation bound for input-free central nodes
Read the full entry →Quantum information · Theory and numerical analysis
Many-body entanglement quantification in arbitrary states through a few partial-transpose moments
arXiv:2610.36156v1 ↗PDF ↗Submitted 26 October 2026
- Question
- Logarithmic negativity quantifies entanglement in mixed states, but computing it needs the full spectrum of the partial transpose and hence tomography. Moments of the partial transpose can be measured with randomized measurements or swap circuits. Given a few such moments, what is the largest amount of negativity they certify?
- Result
- Treating the normalized squared eigenvalues of the partial transpose as a probability measure turns the question into a truncated Hausdorff moment problem, solved exactly by Gauss or Gauss–Radau quadrature. The moments \(p_2,\dots,p_K\) give the best possible lower bound \(\mathcal E_K\). The bounds increase strictly until they become exact at \(K=4s\), where \(s\) is the number of distinct eigenvalue magnitudes, and converge for every state. For \(K=4\) the method reproduces the known bound \(\tfrac12\ln(p_2^3/p_4)\) and shows it is optimal.
Methods Hermite interpolation certificate for moment problems; Saturation by counting spectral levels
Read the full entry →Quantum computing · Theory and numerical analysis
Self-Correcting 3D Surface Code with Growing Local Dimension
arXiv:2610.35099v1 ↗PDF ↗Submitted 26 October 2026
- Question
- A self-correcting quantum memory keeps information for a time growing exponentially in a power of its size under local thermal dynamics, with no active correction. The 4D toric code achieves this, but in three dimensions a no-go theorem for fixed local dimension and the string-like logical operator of the 3D surface code stand in the way. Does allowing the local dimension \(q\) to grow with system size help?
- Result
- Yes. Changing only the Pauli powers of the 3D surface code along one axis, so that its string-like logical operator carries powers \(1,2,4,\dots\) modulo \(q\), gives a translation-invariant code in which, with odd \(q\ge cL^3\) and below a critical temperature, both error sectors have memory time at least \(e^{\Omega(N^{1/3})}\) under single-qudit Metropolis dynamics. Numerics suggest \(\log t_{\rm mem}\sim\min\{q,N^{1/3}\}\), so much smaller \(q\) may suffice.
Methods Weighted chain complexes: change powers, keep supports; Energy against entropy, with a Lee-weight Boltzmann sum
Read the full entry →Foundations of quantum mechanics · Theory
Bargmann-invariant witness of the graviton commutator
arXiv:2610.35253v1 ↗PDF ↗Submitted 26 October 2026
- Question
- Experiments proposed to show that gravity is quantum look for gravitationally induced entanglement or decoherence, but Newtonian entangling phases can be mimicked by assigning a classical field to each branch, and decoherence can be mimicked by classical noise. Is there an interference observable that no branchwise-definite classical gravitational field can reproduce?
- Result
- Yes. For matter coupled linearly to linearized gravity, each branch coherence factorizes exactly into a conservative phase, the characteristic functional of the graviton state, and a phase from the field commutator. For two interferometers, the phase \(\mathfrak B\) of a four-cycle Bargmann invariant cancels everything except the commutator: it is independent of the graviton state and of all Newtonian interactions, and it vanishes for every branchwise-definite classical model. It is bounded by which-path decoherence, \(\mathfrak B^2\le16\,\Gamma_X\Gamma_Y\).
Methods A cycle of coherences that cancels everything classical; Bounding a commutator signal by decoherence
Read the full entry →Quantum information · Theory and numerical analysis
Quantum-enhanced metrology with classical shadows
arXiv:2610.35632v1 ↗PDF ↗Submitted 26 October 2026
- Question
- Reaching the best precision in quantum metrology usually requires measuring a specific, often complicated observable tailored to the probe and encoding. Can one instead measure every qubit in random Pauli bases, as in classical shadows, and still estimate a parameter well, and how much entanglement advantage survives?
- Result
- Yes, with a quantified cost. Combining all Pauli moments up to weight \(K\) from one randomized data set by generalized least squares gives variance \(1/(n\mathcal I)\), where the shadow information \(\mathcal I\) has a closed form. Separable probes reach at most \(\mathcal I=N/3\), so exceeding it witnesses entanglement, and no probe exceeds \(2N^2/(N+2)<2N\). Entanglement therefore gives a constant-factor gain, at most 6, not Heisenberg scaling: about 15% for twisted probes of 12 qubits.
Methods Generalized least squares over correlated shadow moments; Separable benchmark for witnessing useful entanglement
Read the full entry →Quantum information · Theory
Distillable entanglement is continuous
arXiv:2610.35722v1 ↗PDF ↗Submitted 26 October 2026
- Question
- Distillable entanglement, the best rate at which copies of a state can be turned into Bell pairs by local operations and classical communication, is defined operationally and has no single-letter formula. It was known to be lower semicontinuous and continuous on the interior of distillable states, but not continuous in general. Is it continuous everywhere, with an explicit bound?
- Result
- Yes. For states within trace distance \(\varepsilon<1/16\), \[|E_D(\rho)-E_D(\sigma)|\le4\sqrt\varepsilon\log d+4h(\sqrt\varepsilon),\] with \(d\) the smaller local dimension. The same bound holds for entanglement cost. The proof builds an explicit LOCC protocol that converts copies of \(\sigma\) into copies of \(\rho\) using a number of ebits per copy that vanishes as the states approach each other.
Methods Continuity by a cheap conversion protocol; Locating rare outcomes with Grover search instead of measuring every copy
Read the full entry →Foundations of quantum mechanics · Theory
Exact Identification of Quantum Correlations in the Minimal Bell Scenario
arXiv:2610.34364v1 ↗PDF ↗Submitted 25 October 2026
- Question
- In the simplest Bell experiment, two parties with two binary measurements each, the extreme points of the quantum set are known, but deciding whether a given list of eight statistics is quantum still requires searching over mixtures of many of them or climbing a semidefinite hierarchy that converges only in the limit. Is there an exact, finite test?
- Result
- Yes. A behaviour is quantum if and only if it is a mixture of a single behaviour produced by projective measurements on a pure two-qubit state and a local (classical) behaviour. The key step is a proof that every Bell functional with a strict quantum advantage has exactly one quantum maximizer. Membership then reduces to a system of trigonometric equations in five angles, and every quantum behaviour can be realized in dimension \(6\times6\).
Methods A same-marginal local model that dominates every correlator; Eliminating mixture weights to test membership with five equations in five angles
Read the full entry →Quantum computing · Theory
Ancilla-free optimal quantum adder
arXiv:2610.34446v1 ↗PDF ↗Submitted 25 October 2026
- Question
- Quantum addition sits inside factoring, discrete logarithms and many oracles. Ripple-carry adders need no extra qubits but have linear depth; carry-lookahead adders reach logarithmic depth only with extra workspace. Can an exact \(n\)-bit adder have \(O(n)\) gates and \(O(\log n)\) depth with no ancillary qubits at all?
- Result
- Yes. Using only X, CNOT and Toffoli gates with all-to-all connectivity, the paper builds an exact ancilla-free adder with \(O(n)\) gates and \(O(\log n)\) depth, which is optimal for both. A simpler recursive version achieves \(O(n\log\log n)\) gates at the same depth. The construction borrows existing control and data wires as dirty workspace and always restores them.
Methods Echoes: apply a map using dirty borrowed bits and restore them; Reducing addition to two controlled ladders
Read the full entry →Foundations of quantum mechanics · Theory
Finite Nonsignalling Resources Suffice to Simulate Entangled Qubits
arXiv:2610.32319v1 ↗PDF ↗Submitted 23 October 2026
- Question
- One PR box (a binary-input nonsignalling resource) plus shared randomness reproduces all projective-measurement statistics of a maximally entangled qubit pair. Some partially entangled states cannot be simulated with one PR box, and every known exact protocol for them uses a box with real-valued inputs. Is a continuous input alphabet necessary, as Gisin asked?
- Result
- No. For every pure state \(\cos\theta|00\rangle+\sin\theta|11\rangle\), shared randomness and at most \(K(\theta)=4\lceil\sqrt2\pi\cot^2\theta\rceil^2\le128\cot^4\theta\) PR boxes, used in parallel, reproduce all local projective statistics exactly, without communication or postselection. The budget does not depend on the measurement settings. The construction extends to every mixed two-qubit state and to all binary-outcome POVMs.
Methods Exact sampling from an input-dependent density using a fixed shared list; A random-access index box from parallel PR boxes
Read the full entry →Quantum computing · Experiment
Entangled logical qubits on a superconducting quantum processor
arXiv:2610.32347v1 ↗PDF ↗Submitted 23 October 2026
- Question
- On large superconducting chips, two effects not handled by standard surface-code circuits limit logical performance: leakage out of the qubit subspace and a fraction of underperforming qubits and couplers. Can a 120-qubit IBM processor with fast reset support logical memories, entangling operations and teleportation at useful fidelity?
- Result
- Yes. On ibm_phoenix, excluding bad components by re-purposing ancillas halves the distance-5 logical error per round from 1.9% to 0.9%, comparable to the best distance-3 patches. Lattice surgery between adjacent distance-3 codes gives logical Bell-state fidelity above 93%. Three logical qubits give state, Bell-pair and gate teleportation at 78–93%. A stability experiment with resets on every qubit every two rounds reaches about \(2\times10^{-7}\) failure probability at 170 rounds.
Methods Bounding Bell-state fidelity from two stabilizer expectations; Ancilla re-purposing with gauge checks
Read the full entry →Quantum computing · Theory
Elementary proofs of quantum lower bounds for element distinctness and k-sum
arXiv:2610.32693v1 ↗PDF ↗Submitted 23 October 2026
- Question
- Element distinctness needs \(\Theta(n^{2/3})\) quantum queries, but the known lower-bound proofs use the polynomial method, negative-weight adversaries or compressed oracles. The \(k\)-sum bound \(\Omega(n^{k/(k+1)})\) needs the negative-weight adversary. Can these bounds be proved with basic linear algebra?
- Result
- Yes, in under two pages each. Refining the hybrid argument of Bennett, Bernstein, Brassard and Vazirani, the proof tracks second-order differences of algorithm states under changes to two input positions. This gives \(E\|\psi_T(y)-\psi_T(x)\|^2=O(T/n+T^3/n^2)\) between a distinct input and one with a planted collision, hence \(T=\Omega(n^{2/3})\). With \(k\)th-order differences the same scheme gives \(\Omega(n^{k/(k+1)})\) for \(k\)-sum over groups with \(|G|\ge n^k\).
Methods Hybrid argument with a sensitivity budget; Higher-order differences driven only by lower-order ones
Read the full entry →Quantum information · Theory and numerical analysis
Optimal probes for estimating the dephasing of a quantum spin system
arXiv:2610.32724v1 ↗PDF ↗Submitted 23 October 2026
- Question
- To estimate the strength of dephasing on a spin \(J\) (or \(2J\) qubits), which superposition of levels should be prepared? A spin cat state is optimal for weak Gaussian phase diffusion, but its coherence is the first to decay. Over what range does the cat stay optimal, and what works beyond it?
- Result
- For general dephasing channels, the QFI is concave in the probe populations and an ancilla never helps. The channel QFI is a second-order cone program whose dual variables are the optimal populations. For Gaussian diffusion the cat is globally optimal exactly for \(\Delta\le0.1424\) at \(J=1\) and \(\Delta\le0.065\) at \(J=3/2\); for larger \(J\) its range shrinks at least as \(1/J^2\). Beyond it, uniform superpositions, or a one-parameter interpolation between cat and uniform, are near optimal.
Methods Concavity of the QFI in probe populations; Channel QFI as a cone program whose dual is the optimal probe
Read the full entry →Quantum information · Theory
One-sided-DIQKD using any pure bipartite entangled state secure against all attacks
arXiv:2610.32923v1 ↗PDF ↗Submitted 23 October 2026
- Question
- In one-sided device-independent QKD, Bob’s measurements are trusted and Alice’s device is a black box, so security rests on quantum steering. Existing protocols use maximally entangled states, which are costly to make. Can every pure entangled state of any dimension yield a secret key in this setting, including with lossy detectors and noisy sources?
- Result
- Yes. In the noiseless case, self-testing of any pure state \(\sum_i\alpha_i|ii\rangle\) gives a key rate equal to its entanglement entropy. With depolarizing visibility \(\nu\) and efficiency \(\eta\) on Alice’s side, an entropic-uncertainty bound gives a closed-form rate that is affine in \(\eta\), and hence a critical efficiency for every pure state and visibility. The critical efficiency is 1/2 for maximally entangled states and rises only slowly as entanglement falls.
Methods Key rate from the uncertainty relation with a trusted side; Critical efficiency from an affine rate, and a check on the printed formula
Read the full entry →Foundations of quantum mechanics · Theory and numerical analysis
Certain Quantum States Already Require Quantum Time Evolution
arXiv:2610.32937v1 ↗PDF ↗Submitted 23 October 2026
- Question
- Bell tests check quantum theory without assuming a model, but only its static structure. Could the dynamics be tested the same way? In phase-space theories where states are quasi-probability distributions and evolution is given by a generalized bracket, does the presence of certain states in the theory force the bracket to be the quantum (Moyal) one?
- Result
- Yes. Requiring that position and momentum marginals stay nonnegative under anharmonic evolution ties states to dynamics. If a particular superposition of the lowest three oscillator states is admissible, the bracket must be the Moyal bracket to all orders in \(\hbar^2\). If only the first excited oscillator state is admissible, the leading correction must equal the quantum value \(a_1=-1/24\). The ground state alone allows any \(a_1\) between the classical value 0 and \(-1/24\).
Methods Positivity of marginals under evolution as a consistency test between states and dynamics; Zeros of a marginal as a short-time probe of higher-order terms
Read the full entry →Quantum information · Theory with formal verification
FVQKD: A Formal Verification of Quantum Key Distribution Security in Rocq
arXiv:2610.30645v1 ↗PDF ↗Submitted 22 October 2026
- Question
- QKD security rests on hand-checked proofs that chain smooth entropies, an entropic uncertainty relation, a sampling bound and the leftover hash lemma, drawn from several papers with differing conventions. Can the composable finite-key security of BB84 be machine-checked end to end, from a formal protocol program to the key-length theorem?
- Result
- Yes, in FVQKD, a Rocq development of about 151,000 lines, 102,000 of them new, with no admitted lemmas and only the kernel plus three standard axioms. It proves composable finite-key security of BB84 at the tight Tomamichel et al. bound, for every initial state and every adversary channel acting on a formally specified protocol program. Mechanization exposed a missing case in the published argument: after conditioning on the test passing, the smoothing parameter \(\varepsilon/\sqrt{p_{\rm pass}}\) can exceed 1, outside the domain of the uncertainty relation. A second proof branch using the abort probability repairs it, and the key-length formula is unchanged. A concrete instance with \(n=k=10^4\) certifies a 2000-bit key.
Methods The finite-key bound as a chain of entropy inequalities; Split on the event probability when conditioning inflates a smoothing parameter
Read the full entry →Foundations of quantum mechanics · Theory
Entanglement certification of attosecond light fields with photoelectron interferometry
arXiv:2610.31187v1 ↗PDF ↗Submitted 22 October 2026
- Question
- High-harmonic generation is predicted to entangle the infrared driving field with extreme-ultraviolet harmonics. Standard optical certification needs local oscillators or photon-correlation detectors that barely exist at XUV frequencies. Can photoelectron interferometry (RABBIT), already routine in attosecond science, certify that entanglement on its own?
- Result
- Not from one sideband: every set of single-sideband moments has a fully separable explanation. Adding the two neighbouring sidebands supplies moments \(U\) and \(V\), and \(|Q|^2>UV\) then certifies IR–XUV entanglement through the partial transpose. A further bound \(|Q|>H(U,V)\) certifies genuine three-mode entanglement and is tight when \(U=0\). On model states, a displaced two-mode squeezed state is certified only in a window of displacement and squeezing, and a non-Gaussian GME family only for squeezing \(r<0.043\).
Methods Partial-transpose moment matrices from the measured orderings; Biseparable bounds by isolating one Fock sector
Read the full entry →Foundations of quantum mechanics · Theory and numerical analysis
Local Dephasing Sustains Continuous Time Crystals in a Spin-1/2 Ensemble
arXiv:2610.31230v1 ↗PDF ↗Submitted 22 October 2026
- Question
- Pure dephasing destroys single-spin coherence and is normally counted as loss. In a fully connected ferromagnetic spin-\(1/2\) ensemble with local decay, can dephasing instead be what keeps a collective oscillation going, a continuous time crystal under time-independent dynamics?
- Result
- Yes. An exact operator identity shows that dephasing feeds energy into the transverse interaction, which local decay removes with a delay of order \(1/\Gamma_1\). In homogeneous mean field there is no periodic orbit without dephasing, and on a periodic orbit the delayed feedback exactly pays for the transverse damping. Liouvillian spectra for \(N=80\)–\(300\) show oscillatory decay rates falling as \(N^{-0.32}\) and \(N^{-0.46}\), with frequencies approaching the mean-field values.
Methods Exact energy balance from an observable that commutes with the Hamiltonian; Cycle work of a lagged feedback variable
Read the full entry →Quantum information · Theory
Reset-Enhanced Dissipative Quantum Metrology
arXiv:2610.31249v1 ↗PDF ↗Submitted 22 October 2026
- Question
- Dissipation in open quantum sensors usually washes out parameter information. Can the simplest dissipative control, a channel that resets the probe to a fixed state at rate \(r\), increase the quantum Fisher information in steady-state and transient sensing without changing the Hamiltonian or adding a coherent drive?
- Result
- Sometimes, and the paper says exactly when. An exact identity for \(\partial_rF\) gives a first-order test for local enhancement. For a thermal qubit reset to its ground state, steady-state thermometry improves if and only if \(0<\beta\omega<\ln(2+\sqrt5)\) and \(r\) is below a threshold, with optimum \(r_{\rm opt}=\gamma(2+\sqrt5-e^{\beta\omega})/(e^{\beta\omega}-1)\). For diagonal dynamics, reset cannot change the leading short-time Fisher information of a static parameter, but it raises elapsed-time information immediately, roughly as \(r^2\). For frequency estimation with reset to \(|+\rangle\), the gain at \(t=1/\gamma\) is about 7 times, 91% of it from the coherence (eigenvector) part.
Methods Response of the QFI to a control parameter through the SLD; Short-time expansion separating static parameters from time
Read the full entry →Quantum computing · Theory
The Impact of Markovian Errors on Random Circuits
arXiv:2610.31500v1 ↗PDF ↗Submitted 22 October 2026
- Question
- Randomized benchmarking reports one error rate, but under gate-dependent noise it is unclear what that number measures. Average gate infidelity is gauge dependent, so it cannot be the answer. For small Markovian errors, how does each elementary error (Pauli-stochastic, over-rotation, axis tilt) enter the RB decay?
- Result
- For any gate set and sampling distribution forming a sequence-asymptotic unitary 2-design, Pauli-stochastic rates are the only errors that enter the decay linearly. Hamiltonian rates enter through a quadratic form that vanishes on gauge directions. For direct RB of \(\{X_{\pi/2},Y_{\pi/2}\}\) with probability \(p\) of \(X\), the form is explicit in two over-rotations and one relative axis tilt. Equal over-rotations \(\theta\) give \(r=3\theta^2/4\) at \(p=1/2\), three times each gate’s infidelity, and about 16.6 times at \(p=0.9\). For Clifford RB, a fixed form with weights \(1/9\) and \(1/18\) is filtered through the compilation.
Methods First-order RB decay from a Choi-space projector; Gauge invariance forces the coherent term onto FOGI coordinates
Read the full entry →Quantum computing · Theory and numerical analysis
Problem-aware sampling for bias and variance reduction in randomised Hamiltonian simulation
arXiv:2610.31515v1 ↗PDF ↗Submitted 22 October 2026
- Question
- qDRIFT approximates \(e^{-iHT}\) by random Pauli rotations sampled in proportion to \(|c_j|\), ignoring the initial state and the observable. Its estimators carry bias and variance that cost many steps and trajectories. When the goal is a single \(\langle O(T)\rangle\) from a known initial state, can the sampling distribution be tuned to the problem while keeping qDRIFT’s guarantees?
- Result
- Yes, with StateDRIFT. To fourth order in \(dt\), bias and variance depend on the distribution only through a few \(t=0\) quantities built from \(|\psi\rangle\), \(O\) and the Hamiltonian terms. This gives closed-form variance-optimal rules, an interpolating family that provably improves both bias and variance at one step for sign-definite inputs, and an optimized family for deeper circuits. For molecules of 6 to 18 qubits the dynamics resolves in 1.7–26 times fewer steps and 1.2–11 times fewer two-qubit gates; for BeH\(_2\) the gate count falls from 11,201 to 983. Mixing with 20% of the vanilla distribution bounds every reweighting by a factor of 5.
Methods Neyman allocation for importance-sampled channels; Majorana degree counting fixes the RDM order
Read the full entry →Foundations of quantum mechanics · Theory and numerical analysis
Discrete Time Liquids
arXiv:2610.30266v1 ↗PDF ↗Submitted 21 October 2026
- Question
- Time crystals break the discrete time-translation symmetry of a perfectly periodic drive. Can temporal order also emerge from noise, when the only drive is the thermal fluctuation of a cavity mode with finite coherence time?
- Result
- Yes. A two-dimensional classical spin lattice coupled to a thermal cavity mode locks to half the cavity frequency within a window of bath temperatures. When the cavity coherence time is short, single trajectories switch stochastically between the two period-doubled configurations. These switches, called time-solitons, destroy long-range temporal coherence while preserving local period doubling: a discrete time liquid. A one-parameter toy model with independent sign flips reproduces the full distribution of single-trajectory correlation times.
Methods Treat a narrow-band thermal mode as a random-amplitude, random-phase drive; Separate defects from decay with three nested correlation times
Read the full entry →Quantum computing · Theory and numerical analysis
Transversal syndrome extraction: A unifying construction for measuring the error syndromes of any stabilizer code
arXiv:2610.30279v1 ↗PDF ↗Submitted 21 October 2026
- Question
- Fault-tolerant syndrome extraction for a general stabilizer code is either deep (Shor’s method measures one stabilizer at a time with cat states) or wide (Steane’s method measures everything at once with a \(2n\)-qubit encoded ancilla). Configurable middle grounds were known only for CSS codes. Is there one for every stabilizer code?
- Result
- Yes. Partitioning the stabilizer generators into sets measured together, and building a matching ancilla stabilizer state from the generalized Steane ancilla, gives a family of transversal gadgets for any stabilizer code. Shor and Steane extraction appear as the two limits, so depth can be traded for width. For example, the full syndrome of an \([[8,2,3]]\) code can be measured with four layers of data–ancilla gates using at most 12 ancilla qubits. Simulated logical error rates fall between those of Shor and Steane extraction.
Methods Design ancillas so that propagated stabilizers carry the syndrome and nothing else; Interpolate between two known gadgets by deleting rows and qubits
Read the full entry →Quantum information · Theory
Pure states are optimal for total energy-constrained quantum channel discrimination
arXiv:2610.30295v1 ↗PDF ↗Submitted 21 October 2026
- Question
- When discriminating two bosonic channels with a probe of fixed mean photon number and no ancilla, is a pure probe always optimal? Convexity suggests yes, but the pure components of a mixed probe generally have different photon numbers, so the best component may break the energy budget.
- Result
- Yes. Every state of mean photon number \(\bar n\) is a mixture of pure states each with mean photon number exactly \(\bar n\), including for infinite rank. Combined with Lieb concavity, this shows that for any two channels some equal-energy pure probe does at least as well as any mixed probe. This holds for the quantum Chernoff exponent, for every Chernoff quantity \(Q_s\), and for the single-shot error probability.
Methods Equalize a constraint across a decomposition by pairwise rotations; From concavity at one \(s\) to optimality of the minimized exponent
Read the full entry →Quantum computing · Theory and numerical analysis
Normal-Form Characterization of Adaptivity and Entanglement in Pauli-Based Computation
arXiv:2610.30315v1 ↗PDF ↗Submitted 21 October 2026
- Question
- Pauli-based computation (PBC) runs a Clifford+\(T\) circuit as a sequence of commuting Pauli measurements on magic states, chosen adaptively from earlier outcomes. The adaptive tree of measurements is exponentially large. Is there a compact description of how branches differ, comparable to flow in one-way computing?
- Result
- Yes. Every branch of the PBC tree is obtained from the all-zero reference branch by conjugating each observable with phase gates \(S\) on the magic qubits whose earlier outcomes were 1. This normal form groups measurements into adaptive layers, gives a duality with a computation-specific one-way computation, detects unnecessary magic qubits in polynomial rather than exponential time, and allows ahead-of-time compilation. The resulting circuits use on average about 50% fewer CNOTs and 40% less quantum memory than state-of-the-art compilers on random circuits.
Methods Move outcome-dependent corrections onto the input state; Detect removable resources by checking one branch against a symmetry
Read the full entry →Quantum information · Proposal
Distributed dual-comb spectroscopy
arXiv:2610.30462v1 ↗PDF ↗Submitted 21 October 2026
- Question
- Quantum-enhanced dual-comb spectroscopy uses squeezed or entangled frequency combs to beat shot noise over a broad band, and distributed quantum sensing uses entanglement across sites to estimate global quantities. Can one combine both, estimating weighted averages of absorption across many samples and many frequencies, with a single quantum light source?
- Result
- Yes. Each sample sits in a Mach–Zehnder interferometer with a bright classical comb in one port and a share of a single two-mode-squeezed comb, split \(K\) ways by a passive beam splitter, in the dark port. With splitter weights matched to the target weights, the variance of every weighted-average estimator falls by the squeezing gain \(G\). Splitters that do not depend on frequency force a trade-off between gases with different targets: for orthogonal targets the guaranteed advantage is \(2G/(G+1)\), at most 3 dB.
Methods Match the entanglement splitter to the estimated linear functional; Bound multi-target advantage by a shared-resource geometry
Read the full entry →Foundations of quantum mechanics · Review
Photon localization: Local measurements, localized states, and causality
arXiv:2610.30473v1 ↗PDF ↗Submitted 21 October 2026
- Question
- What does it mean for a photon to be localized in quantum field theory, where there is no position operator, the vacuum is entangled across regions, and no-go theorems (Hegerfeldt, Malament, Reeh–Schlieder) seem to forbid localized particles altogether?
- Result
- The review argues that localization should be defined through local measurement: a state is strictly localized to a spacetime region \(\mathcal O\) if no observable outside \(\mathcal O\) can tell it from the vacuum. With this definition, single photons (and any state with a bounded photon number) cannot be strictly localized, while coherent states, squeezed states and states arbitrarily close to single photons can. On-demand sources must produce strictly localized states.
Methods Prove non-localizability from a nonvanishing vacuum matrix element; Build localized states from the polar part of a smeared field
Read the full entry →Quantum information · Theory
A simple proof of unitary parallelization via port-based teleportation
arXiv:2610.30761v1 ↗PDF ↗Submitted 22 October 2026
- Question
- Can port-based teleportation be implemented by an elementary low-depth circuit, and does that give a simple proof that every unitary can be parallelized?
- Result
- Yes. A single reflection on Alice’s registers implements port-based teleportation with \(N\) ports and dimension \(d\) to diamond error \(2(d^2-1)/N+\delta\), in depth \(\operatorname{polylog}(Nd/\delta)\). Feeding Choi states of \(U\) into the ports implements any \(n\)-qubit unitary in depth \(\operatorname{poly}(n,\log1/\varepsilon)\) and width \(2^{O(n)}\operatorname{poly}(1/\varepsilon)\).
Methods Teleport with a single reflection; Read out sums of swaps with parallel random SWAP tests
Read the full entry →Quantum computing · Theory and computer-assisted proof
The limits of magic-state distillation
arXiv:2610.31115v1 ↗PDF ↗Submitted 22 October 2026
- Question
- How few noisy T states can any stabilizer protocol, however adaptive, postselected or multistage, consume to output a magic state with error \(O(p^d)\)?
- Result
- Exact minima for small factories. Fault tolerance of any protocol reduces to projection onto a single stabilizer code, and for rational targets a fault pattern is harmful exactly when its complement is. Exhaustive search then shows: quadratic distillation of one T state needs exactly 9 inputs (a new 9-input factory is found), controlled-S needs 8, and the 8-input CCZ factory is optimal. At every order \(d\), one T state needs at least \(2d\) inputs.
Methods Reduce all protocols to one code projection; Galois conjugation pairs complementary faults
Read the full entry →Quantum information · Theory
One-shot entanglement generation and distillation via Petz recovery and binary hypothesis testing
arXiv:2610.31501v1 ↗PDF ↗Submitted 22 October 2026
- Question
- How much entanglement can two laboratories obtain from one use of a noisy channel or one copy of a shared noisy state, and can the answer be expressed as a binary hypothesis-testing cost?
- Result
- An \((m,\varepsilon)\) entanglement generation or one-way distillation protocol exists whenever \(e_{d,m}(1-e_{d,m}/dm)\le\varepsilon\). Here \(e_{d,m}\) is the optimal error for testing \(\rho_{AB}\) against an explicit alternative \(B_{d,m}\propto dI_A\otimes\rho_B-\rho_{AB}\). Consequently \(\log_2m\le I_H^{\varepsilon-\nu}(A\rangle B)-\log_2(1/\nu)\) suffices, and repeated use gives \(nI_c+\sqrt{nV_c}\,\Phi^{-1}(\varepsilon)-\tfrac12\log_2n-c\) ebits.
Methods Apply Cheng’s trace inequality before averaging over random codes; From a binary test to an integer code dimension
Read the full entry →Quantum computing · Theory
Size-independent Logarithmic Sobolev Inequalities for Quantum Gibbs Samplers
arXiv:2610.31571v1 ↗PDF ↗Submitted 22 October 2026
- Question
- Does relative entropy decay at a rate independent of system size under quasi-local quantum Gibbs samplers for non-commuting Hamiltonians?
- Result
- Yes, in two regimes. For the Gaussian KMS Gibbs sampler, both the \(L^2\) logarithmic Sobolev inequality and the modified one (MLSI) hold with system-size-independent constants: in one dimension at every finite temperature, and in any fixed dimension at sufficiently high temperature. This gives \(O(\log n+\log(1/\epsilon))\) mixing time.
Methods Transport a functional inequality along a unitary path; Upgrade Rényi-2 contraction to relative-entropy contraction with tensor powers
Read the full entry →Foundations of quantum mechanics · Theory and numerical analysis
Mixed State Deep Thermalization under Generic Quantum Errors
arXiv:2610.31580v1 ↗PDF ↗Submitted 22 October 2026
- Question
- After chaotic dynamics, the states of a subsystem conditioned on measuring the rest follow a universal (Haar) distribution. What distribution emerges when local errors make those conditional states mixed?
- Result
- A universal one fixed by the error alone. The late-time ensemble of conditional states is the channel-induced ensemble, \(\tilde\rho=XMX^\dagger\) with \(X\) a complex Gaussian (Ginibre) matrix and Born weight \(\operatorname{Tr}XMX^\dagger\). Here \(M\) is the normalized Choi state of the error, and only its spectrum matters. This is derived for dual-unitary circuits, global Haar dynamics and local Haar circuits at large local dimension, and checked numerically in qubit circuits and kicked Ising dynamics.
Methods A random-matrix reference ensemble built from the Choi state; Born-weighted moments of a projected ensemble
Read the full entry →Foundations of quantum mechanics · Conceptual analysis
What does quantum parameter estimation estimate? A no-go result for true quantity values
arXiv:2610.31632v1 ↗PDF ↗Submitted 22 October 2026
- Question
- Quantum metrology speaks of estimating an unknown “true value”. Is that reading consistent when the estimated quantity is itself quantum and can become entangled with the probes?
- Result
- No, not without a cost. Embedding the parameter as an observable \(\hat\theta\) reproduces standard estimation whenever its state is diagonal. But five assumptions cannot all hold together: Uniqueness, Pre-existing Value and Independence (the realist reading of a true value), Entanglement between quantity and probes, and Completeness of the quantum state (no hidden variables). Dropping any one restores consistency.
Methods Embed a classical parameter as a controlling quantum register; Locate a no-go theorem by listing jointly inconsistent assumptions
Read the full entry →Quantum information · Theory
Quantum f-divergences from retrodiction: a unifying classical variational principle
arXiv:2610.29696v1 ↗PDF ↗Submitted 21 October 2026
- Question
- A classical \(f\)-divergence has several inequivalent quantum extensions. Can they all be obtained from one operational optimization?
- Result
- Yes. Compare a forward prepare-and-measure process with its reverse, obtained by Petz retrodiction relative to a reference prior \(\gamma\), subject to prescribed averages \(\rho\) and \(\sigma\). The minimum classical \(f\)-divergence between their complete records is attained by one spectral implementation, simultaneously for every operator-convex \(f\). A flat prior gives the standard (Petz) divergence, Umegaki for relative entropy. A prior equal to \(\rho\) or \(\sigma\) gives the maximal divergence, Belavkin–Staszewski for relative entropy, and power priors \(\gamma\propto\sigma^t\) give the geodesic family between them.
Methods Two operator-Jensen steps remove the implementation freedom; The retrodiction prior selects the quantum divergence
Read the full entry →Foundations of quantum mechanics · Conceptual analysis
Conservation in Every Quantum Measurement Outcome?
arXiv:2610.29804v1 ↗PDF ↗Submitted 21 October 2026
- Question
- Does including the system that prepared a superposition restore a conservation law in every individual measurement outcome, as Collins and Popescu have proposed?
- Result
- The authors argue that it does not, in the sense claimed. The need for a physical preparer is postulated rather than derived from the relativity of angle. The preparer never holds a definite value, so what the mechanism restores is a shifted probability distribution. A preparation that conserves one observable can disturb a noncommuting one. For energy, the preparation interaction breaks the additivity the bookkeeping relies on.
Methods Test a conservation mechanism against the whole symmetry group; Overlap factors set how broad a hidden partner must be
Read the full entry →Quantum computing · Theory with formal verification
Finite Classification of Transversal Diagonal Gates Beyond Stabilizer Codes
arXiv:2610.29955v1 ↗PDF ↗Submitted 21 October 2026
- Question
- Code-preserving diagonal phases of general (nonadditive) qubit codes can vary continuously. Can the transversal diagonal gates of such codes still be classified exhaustively?
- Result
- Yes, at fixed code parameters. For a code of distance at least two, every projective logical action of a transversal diagonal gate has a physical representative of finite order \(q\), with \(m\mid q\) and \(q\) bounded in terms of \(n\) and \(K\) alone; \(q\le9\) for six qubits at distance three. For exact ((6,2,3)) codes, 66 candidate symmetry classes reduce to 15 realizable ones, with diagonal logical groups \(C_2\), \(C_3\) or \(C_5\). The order-five code is unique up to local unitaries and qubit permutations. It is also the shortest distance-3 qubit code whose transversal logical group cannot be conjugated into the Clifford group.
Methods Strip continuous phases that act only as logical scalars; Subset-sum sectors and moment matching as a staged filter
Read the full entry →Foundations of quantum mechanics · Theory and numerical analysis
An entanglement band structure for general multiqubit states
arXiv:2610.30040v1 ↗PDF ↗Submitted 21 October 2026
- Question
- Majorana pictured a symmetric multiqubit state as points on the sphere. Can a comparable geometric picture be given for general states, whose entanglement classes form continuous families?
- Result
- Projecting one qubit onto a direction \(\mathbf n\) leaves a conditional state of the others. Its entanglement invariants are the eigenvalues, called bands, of a non-Hermitian matrix \(L(u)\). For five qubits there are four bands, which meet at 24 exceptional points where the conditional state changes entanglement family. Together they form one Riemann surface of genus nine, which fixes the five-qubit entanglement class up to finitely many choices.
Methods Read SLOCC invariants from a holomorphic matrix pencil; Count exceptional points and the genus from the discriminant
Read the full entry →Quantum information · Theory
Tight Bounds on the Randomized Communication Complexity of Vector-in-Subspace
arXiv:2610.30052v1 ↗PDF ↗Submitted 21 October 2026
- Question
- One quantum message of \(\lceil\log_2n\rceil\) qubits solves Vector-in-Subspace exactly. How many bits does an interactive classical protocol need?
- Result
- \(\Theta(\sqrt n)\) bits. A lower bound of \(\Omega(\sqrt n)\) holds for bounded-error randomized protocols with any number of rounds, matching Raz’s \(O(\sqrt n)\) protocol. It improves the \(\Omega(n^{1/3})\) bound of Klartag and Regev and removes the total-rank restriction in Grupel’s \(\Omega(\sqrt n)\) result.
Methods Complex Gaussian lifts perform the Wick corrections; A vanishing even moment bounds a real center
Read the full entry →Quantum computing · Theory and numerical analysis
Injection is all you need: parallel universal logic in high-rate concatenated self-dual codes
arXiv:2610.30087v1 ↗PDF ↗Submitted 21 October 2026
- Question
- High-rate codes store many logical qubits per block but make it hard to act on a chosen subset. How can they run parallel, addressable, universal logic?
- Result
- In concatenated self-dual codes with transversal global \(H\) and \(S\), any logical Clifford is injected by consuming at most 9 CSS resource states. \(T\) gates on any subset need one \(\ket H^{\otimes K}\) magic state and one CSS state, so a circuit of \(T\)-depth \(D_T\) needs at most \(12D_T\) resource states. A Hadamard parity check repeated at each concatenation level gives magic states whose undetected error is \(O(p^{2^L})\). In simulations at \(p=5\times10^{-4}\), this concatenated cultivation needed about ten times less spacetime than surface-code cultivation for the two distance-4 codes.
Methods Reduce every Clifford layer to CSS resource states; Hadamard-parity flags, and why one parity stalls at second order
Read the full entry →Quantum information · Experiment
Trapped-ion-based quantum repeater node across a 17 km metropolitan fiber
arXiv:2610.27854v1 ↗PDF ↗Submitted 20 October 2026
- Question
- Can a trapped-ion repeater node distribute entanglement over deployed city fiber rather than a laboratory spool?
- Result
- A two-ion node in Innsbruck entangled a photon sent through 17 km of rented municipal fiber with a photon detected locally. The Bell-state fidelity was \(81.6^{+1.9}_{-1.4}\%\) (with feed-forward simulated), at 0.69 successes per second. Storing the first ion qubit raised the success probability 13.6-fold over sending both photons without memory.
Methods Store the qubit for the fast link, not the slow one; Correct a drifting fiber by tomography and inversion
Read the full entry →Foundations of quantum mechanics · Theory
Dimension-free marginal inequalities for pure three-party states
arXiv:2610.28162v1 ↗PDF ↗Submitted 20 October 2026
- Question
- Which spectra can the three one-party marginals of a pure three-party state have, with inequalities that hold in every local dimension?
- Result
- A lifting theorem produces new valid inequalities from old ones by peeling off one party’s largest Schmidt component and applying Horn’s inequalities to the other two. Starting from Klyachko’s first-row bound, at most two lifting steps reproduce every facet of the marginal polytope for local dimension up to 4, and 455 of the 466 facet classes for dimension 5.
Methods Peel off the largest Schmidt component; Combine Horn triples with Abel summation
Read the full entry →Foundations of quantum mechanics · Theory with formal verification
The Four-Qubit Hyperbolic Quadric Has Contextuality Degree 315
arXiv:2610.26465v1 ↗PDF ↗Submitted 19 October 2026
- Question
- How many of the 1575 three-observable constraints on a four-qubit hyperbolic quadric must every noncontextual value assignment break?
- Result
- Exactly 315, proving a conjecture based on heuristic searches. In every optimal assignment each of the 40,320 doilies has exactly three violated lines, and the 240 possible violated sets are all copies of the dual polar space DW(5,2).
Methods Read a lower bound from parity alone; Average over a symmetric cover, rounding locally
Read the full entry →Quantum computing · Numerical study and analysis
Correlated decoding loses the surface code’s effective distance below threshold
arXiv:2610.26785v1 ↗PDF ↗Submitted 19 October 2026
- Question
- Does two-pass correlated decoding of the surface code keep its advantage far below threshold?
- Result
- Not with the standard reweighting rule. Under circuit-level noise some size-\((d-1)/2\) fault configurations cause logical failures, so the logical error rate scales like \(p^{(d-1)/2}\) instead of \(p^{(d+1)/2}\). At \(d=3\) and \(p=10^{-5}\), correlated matching fails about 4.4 times as often as plain matching. Scaling the conditional edge probabilities by an error-rate-dependent factor \(\alpha^*(p)\) restores the distance scaling and a steady advantage.
Methods Count the independent faults behind a correction; Regularize the update with one error-rate-dependent parameter
Read the full entry →Quantum computing · Theory
Polynomial-Time Classical Simulation of BosonSampling under Any Constant-Fraction Photon Loss
arXiv:2610.27065v1 ↗PDF ↗Submitted 19 October 2026
- Question
- Does lossy BosonSampling remain hard to simulate classically when a fixed fraction of the photons survives?
- Result
- Not under the conditions studied. For every fixed survival fraction \(n/N\in(0,1)\), Haar-random interferometers and \(M=\Omega(n^2N)\) modes, a classical algorithm samples within total variation distance \(\varepsilon\) of the collision-collapsed output distribution, for a \(1-\delta\) fraction of interferometers, in time \(\mathrm{poly}(M,N,\varepsilon^{-1},\delta^{-1})\). The same holds for every fixed transmission probability \(\eta\in(0,1)\).
Methods Decompose an average over random survivors; Sum over subsets with color coding
Read the full entry →Quantum information · Theory
Randomness Certification from Statistically Hiding Commitments
arXiv:2610.25518v1 ↗PDF ↗Submitted 18 October 2026
- Question
- What cryptographic assumption lets a classical verifier certify randomness from a single untrusted quantum device, secure against quantum side information?
- Result
- A statistically hiding bit commitment that is computationally binding against quantum senders suffices; stronger notions such as collapse-binding are not needed. Consequently, post-quantum one-way permutations suffice. Trapdoor claw-free functions give an efficient verifier, and the quantum random-oracle model gives certification with no further assumption but an inefficient verifier.
Methods Hide a BB84 basis inside two commitment openings; Turn a predictor into two openings
Read the full entry →Quantum information · Proposal
Pump-Free Microwave-Optical Bell Pair Generation for Teleportation-Based Quantum Transduction
arXiv:2609.16364v1 ↗PDF ↗Submitted 14 September 2026
- Question
- How can superconducting processors connect to optical networks while avoiding complications from optical pumping?
- Result
- Spin-mediated sources are predicted to herald microwave–optical Bell pairs at roughly 1–28 kHz, with fidelities of 0.86–0.99 depending on the platform. The pairs are intended for teleportation-based transduction.
Methods Separate resource generation from state transfer; Use an intermediate spin as an interface
Read the full entry →Foundations of quantum mechanics · Theory
Information Causality Characterizes the Set of Quantum Correlations in the Simplest Bell Scenario
arXiv:2609.10508v1 ↗PDF ↗Submitted 9 September 2026
- Question
- Can an information principle recover the quantum boundary in the simplest Bell experiment?
- Result
- Generalized information causality implies the Tsirelson–Landau–Masanes criterion on the four renormalized correlators, so it recovers the quantum boundary of that correlator projection. A separate example shows that it also excludes some correlations that macroscopic locality allows.
Methods Keep the full measurement record; Expand around zero capacity
Read the full entry →Foundations of quantum mechanics · Theory
Spurious quantum correlations
arXiv:2609.04157v1 ↗PDF ↗Submitted 3 September 2026
- Question
- Can correlations that appear nonclassical acquire a classical explanation when the assumed causal structure changes?
- Result
- The authors identify correlations with classical explanations in alternative causal structures without fine tuning, and other correlations that resist such explanations.
Methods Search over causal explanations; Separate statistical fit from physical admissibility
Read the full entry →Quantum computing · Theory and numerical analysis
Quantum error correction at ultra-low overhead
arXiv:2608.02773v2 ↗PDF ↗Submitted 3 August 2026
- Question
- Can quantum error-correcting codes combine high encoding rates, tolerable noise, and feasible neutral-atom operations?
- Result
- Cornucopia codes reach encoding rates just above 1/2 at distances 6 to 18 and pseudo-thresholds above 0.4% under circuit-level noise. Their 12-layer syndrome cycle is carried out by rigid moves of whole atom blocks.
Methods Design the code and its circuit together; Certify distance and count resources consistently
Read the full entry →Quantum information · Theory
A solution to 2-copy distillability of Werner states
arXiv:2607.21367v3 ↗PDF ↗Submitted 23 July 2026
- Question
- Can two copies of a Werner state yield distillable entanglement when one copy cannot?
- Result
- For every local dimension \(d\), a Werner state \(\rho_\alpha\) is two-copy distillable exactly when it is one-copy distillable (\(\alpha<-\tfrac12\)). States with \(-\tfrac12\le\alpha<-\tfrac1d\) are therefore NPT but not two-copy distillable.
Methods Turn distillation into an operator test; Use symmetry to isolate a boundary case
Read the full entry →Quantum computing · Experiment
Quantum error correction with the toric code
arXiv:2606.04079v1 ↗PDF ↗Submitted 2 June 2026
- Question
- Can neutral-atom logical memories sustain repeated error correction while replacing lost atoms?
- Result
- Twisted toric-code memories on 32 and 64 atoms (\([[16,1,(4,3)]]\) and \([[32,1,(6,4)]]\)) run for up to 90 and 70 syndrome cycles with atom reloading. Over four to eight cycles, the larger code has the lower logical error.
Methods Rotate data and ancilla roles; Make replenishment part of the computation
Read the full entry →