Papers
Research Papers
Recent arXiv papers in quantum foundations, computing, and information. Each entry states the question and result; its full page explains the paper in detail and the methods worth reusing, with derivations.
120 papers · reviewed 8 November 2026
Selected in November 2026
Quantum computing · Theory and computer-assisted proof
Certifying the Rydberg-exposure limit of a globally driven controlled-Z gate
arXiv:2611.07388v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Neutral-atom CZ gates excite atoms to Rydberg states, and decay from those states is a leading source of gate error and atom loss, with loss probability about \(\Gamma T_R\) for average Rydberg time \(T_R\). Can pulse shaping and longer gates make the exposure \(C=\Omega_{\max}T_R\) arbitrarily small when one global laser drives both atoms, with perfect blockade? Numerical optimal control had reached \(C\approx2.936\), but no lower bound valid for all pulses existed.
- Result
- No: for every exact globally driven CZ gate in the perfect-blockade model, of any duration, \(2.9312\le C_*<2.9359\). The lower bound comes from a sum-of-squares certificate verified exactly over \(\mathbb Q(\sqrt2)\); the upper bound from an interval-arithmetic (Krawczyk) proof that an exact CZ pulse exists near a numerical candidate. The unrounded bounds differ by less than 0.16%.
Methods Exposure lower bounds from a value-function certificate; Interval-certified existence of an exact pulse
Read the full entry →Quantum information · Theory
Efficient Pauli truncation from operator stabilizer Rényi entropy
arXiv:2611.07545v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Classical simulation by Pauli propagation evolves an observable in the Heisenberg picture and keeps only its \(\chi\) largest Pauli coefficients. The operator stabilizer Rényi entropy (OSE) \(M^{(\alpha)}\), the Rényi entropy of the squared Pauli coefficients, measures how spread out those coefficients are. For which Rényi indices does slow OSE growth guarantee that polynomially many terms give accurate expectation values for every input state, and when does fast growth rule it out?
- Result
- Linear growth of \(M^{(1)}\), or power-law growth of \(M^{(\alpha)}\) for \(\alpha>1\), forces superpolynomially many terms for a fixed error over all states. Logarithmic growth for \(0<\alpha<1/2\) guarantees polynomially many terms suffice for every state, and the range is sharp: the operator \(I-2|0^N\rangle\langle0^N|\) has bounded OSE for every \(\alpha\ge1/2\) but needs about \(2^{N}\) terms. Averaged over low-average state ensembles the sufficient range extends to \(0<\alpha<1\). The paper also bounds cumulative error in iterative propagation and fixed-order OTOCs.
Methods Rényi tails control the coefficient tail; Coherent accumulation on a common eigenstate
Read the full entry →Foundations of quantum mechanics · Theory and experiment
Non-unitary quantum butterfly effect: theory and experiment
arXiv:2611.08152v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Out-of-time-order correlators (OTOCs) measure how a local perturbation spreads through a many-body system, and in random unitary circuits they show a ballistic front behind which the signal saturates. Mid-circuit measurements are now routine, but how far and for how long an unread measurement disturbs the rest of a register is poorly characterised. What does the OTOC do when the evolution itself is non-unitary?
- Result
- The authors define an OTOC for quantum channels that bounds how much a perturbation at site \(y\) can change a measured expectation value at \(x\). For brickwork Haar-random circuits of qudits measured at each site with probability \(p\) per layer, the circuit-averaged OTOC is a transfer-matrix contraction. It decays at late times as \(\lambda_*^{t}\) with \(\lambda_*=1-\tfrac{2(q-1)}{q}Np+O(p^{2})\) for \(Np\ll1\), and for sparse measurement in a large system the decay is Gaussian in time with variance \(1/(\kappa p)\). Eight-qubit runs on Quantinuum's H2 resolve the light cone and the decay inside it.
Methods Weighted random walk for the averaged OTOC; Perturbation theory for the gap of the transfer matrix
Read the full entry →Quantum information · Theory
Optimal finite-copy readout of three-qubit entanglement with state retention
arXiv:2611.08233v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Given \(n\) copies of an unknown three-qubit pure state, how likely can a fixed measurement be to certify, without false positives, that the state is in the GHZ class (nonzero three-tangle \(\tau\))? How large can the coefficient be in an event whose probability is exactly proportional to \(\tau^{2}\)? And can such a certificate leave a copy of the unknown state intact?
- Result
- Fewer than four copies give no certificate. Four copies give optimal probability \(\tau^{2}/48\). Five copies give \(5\tau^{2}/72\), a factor \(10/3\) more, and can return the unknown input on success; five is the minimum for that. At six copies certification and exact binary readout first differ: \((39+2S)\tau^{2}/296\) against \(\tau^{2}/8\), where \(S\) is the sum of single-party purities. Local spin measurements with classical communication attain all of these optima.
Methods Multiplication operators fix the optimal effects; Schur's lemma gives the extra-copy gain
Read the full entry →Quantum computing · Theory and numerical analysis
Certifying quantum code and circuit distances at scale
arXiv:2611.08247v1 ↗PDF ↗Submitted 5 November 2026
- Question
- The circuit distance, the fewest faults in a syndrome-extraction circuit that flip a logical observable without firing any detector, sets the leading order of the logical error rate. For qLDPC circuits with \(10^{4}\) to \(10^{5}\) fault mechanisms, papers usually report upper bounds from heuristic searches, and resource estimates for planned machines rest on assumed values. Can exact distances be certified at that scale?
- Result
- Writing both code and circuit distance as a tropical (min-plus) partition function and combining two dynamic programs, a bounded search and certified relaxations, the method certifies 70 of 74 benchmark instances in the authors' suite against 53 for all other exact solvers combined, and 95 against 80 on an independent benchmark. It certifies codes with up to 31,200 qubits and circuits with up to \(8\times10^{5}\) fault mechanisms. An audit of 26 papers finds overestimated distances in 10, with a gap of at least eight. IBM's two-gross \([\![288,12,18]\!]\) memory circuit has circuit distance 16 with the standard schedule, not 18; other schedules reach 18 at one noisy cycle, at the cost of a ninth timestep per cycle.
Methods Min-plus dynamic programming on the syndrome trellis; Relax, then lift: certified lower bounds that meet explicit errors
Read the full entry →Foundations of quantum mechanics · Proposal
Testing gravitationally induced entanglement with massive particles and quantum clocks
arXiv:2611.08313v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Proposed tests of whether gravity can entangle two masses can be explained by the Newtonian potential between fixed masses, which some argue admits a classical, non-local account. A test that needs a relativistic feature of gravity would close that loophole. The contribution of a clock's internal energy to gravitating mass is such a feature, but the entanglement it generates between two clocks takes about \(10^{41}\) s to appear.
- Result
- Replacing one clock by a delocalised levitated particle of about the Planck mass (\(M\sim10^{-8}\) kg), and the other by an array of \(N\) clocks, shortens the time scale by the particle's mass and by \(\sqrt N\). For \(N=10^{23}\) scandium-45 nuclear clocks in a centimetre-scale crystal, 450 µm from a particle delocalised by 0.1 µm, the authors estimate an entanglement (equivalently, dephasing) time of about \(5\times10^{6}\) s, or 64 days (Eq. 9).
Methods Collective which-path dephasing; Summing a slab of clocks
Read the full entry →Quantum information · Theory
Upper and lower bounds for few-copy Gaussian tomography, and the absence of a fermionic warm regime
arXiv:2611.07271v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Learning an \(m\)-mode Gaussian state to trace distance \(\epsilon\) takes \(\Theta(m^2/\epsilon^2)\) copies if all copies can be measured jointly. With one copy at a time, mixed states need more. Chen, Mele, Mele and Preskill showed that for bosons cold states need \(m^3/\epsilon^2\) but warm states only \(m^2/\epsilon^2\). They asked how this temperature crossover looks for finite-dimensional systems. Is there a warm regime for fermions, and what do measurements on blocks of \(k\) copies buy?
- Result
- Fermions have no warm regime: for every \(\beta_0>0\), quadratic Gibbs states with \(\beta\|h\|_F\le\beta_0\) need \(\Theta(m^3/\epsilon^2)\) single-copy samples at accuracies resolving the ball. At the maximally mixed state, blocks of at most \(k\) copies need \[N>\frac{m^3}{8{,}553{,}600\,k\,\epsilon^2}\qquad(\epsilon\le1/3600).\] An exact formula shows that the Fisher budget behind this bound is asymptotically attained. Near the vacuum, blocks need \(\Omega(m^3/(\epsilon^2\min\{\sqrt k,m\}))\). A particle-number measurement followed by the Nayak–Zhou qudit protocol attains this for every \(k\) on number-conserving fermionic and on all cold bosonic Gaussian states.
Methods Replicated-parameter Fisher budget; Exact maximal Fisher information from spinor tensor powers
Read the full entry →Foundations of quantum mechanics · Theory
Extensions of the Haldane gap proof: higher dimensions, near degeneracy, fermions and tensor-network states
arXiv:2611.07400v1 ↗PDF ↗Submitted 5 November 2026
- Question
- A recent paper by OpenAI proved that the spin-one Heisenberg chain is gapped in the thermodynamic limit, using only spectral information from a finite system. The argument, which this paper calls the purity bootstrap, compares the purity of the Gibbs state with that of a dual Gibbs state obtained by exchanging space and imaginary time. Does it work in more than one dimension, for phases with several nearly degenerate ground states, for fermions, and for wave functions rather than Hamiltonians?
- Result
- The bootstrap extends to every spatial dimension: a single finite ratio of partition functions above a fixed threshold certifies a size-independent gap. Summing over symmetry twists lets it handle near degeneracy. Finite calculations show that the 2+1-dimensional transverse-field Ising model for \(h/J\le1.8\) has two low states split by at most \(Ce^{-cL^2}\), and that the toric code in a field with \(h/J_m\le1/7\) has four split by at most \(Ce^{-cL}\), each with a gap above them. A fermionic version establishes a symmetric mass generation phase for \(t/J\le1/35\). For the Jian–Zaletel spin-one PEPS the paper proves a correlation length below 8.012 lattice spacings.
Methods The purity bootstrap; Symmetry twists replace symmetry projections
Read the full entry →Quantum computing · Theory
Structured Quantum Hardness from Unstructured Assumptions
arXiv:2611.07413v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Languages in \(\mathsf{NP}\cap\mathsf{coNP}\) have short checkable certificates for both answers. The classic candidates for hard ones, factoring and discrete logarithm, fall to Shor's algorithm, and lattice assumptions give certificates only on promise inputs. Bennett and Gill asked whether \(\mathsf{NP}\cap\mathsf{coNP}\) stays hard relative to a random oracle. Is there quantum-hard two-sided certification that arises from unstructured sources?
- Result
- If \(\mathsf{UP}\not\subseteq\mathsf{BQP}\), then \(\mathsf{NP}^{\mathcal O}\cap\mathsf{coNP}^{\mathcal O}\not\subseteq\mathsf{BQP}^{\mathcal O}\) with probability one over a random oracle \(\mathcal O\). Along the way the paper builds an unbounded-prover NIZK proof for \(\mathsf{NP}\) in the quantum random oracle model with no further assumptions. In the other direction, no fully black-box quantum reduction derives a worst-case quantum-hard \(\mathsf{NP}\cap\mathsf{coNP}\) problem from post-quantum injective one-way functions and indistinguishability obfuscation.
Methods Strong preimage pseudorandomness; Compressed partially fixed oracle
Read the full entry →Quantum information · Theory
Information-Spectrum General Formulas for the Capacity Region of Classical-Quantum Multiple Access Channels
arXiv:2611.07462v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Two senders transmit classical messages through a channel whose output is a quantum state. For memoryless channels the capacity region is known, but real channels may have memory or change with block length. The information-spectrum method gives capacity formulas for arbitrary channel sequences: Verdú–Han and Hayashi–Nagaoka for one sender, Han (1998) for the classical two-sender channel. For the classical-quantum multiple access channel only an outer bound (Kubo–Nagaoka 2015) was known. What is the exact region?
- Result
- For every sequence of cq-MACs, the capacity region (vanishing error) is the union over input-distribution sequences of the regions \(R_1\le\underline I_1\), \(R_2\le\underline I_2\), \(R_1+R_2\le\underline I_0\), defined by three spectral inf-mutual information rates. This is the quantum counterpart of Han's formula. For every \(0\le\varepsilon<1\), the \(\varepsilon\)-capacity region equals the 2015 outer bound evaluated at the marginal states, so that bound is tight. Its consistency constraint turns out to be unnecessary.
Methods One-shot bounds applied member by member; Threshold tests as a square-root decoder
Read the full entry →Foundations of quantum mechanics · Theory
Exponential mixing time for the Davies dynamics of the quantum random energy model
arXiv:2611.08064v1 ↗PDF ↗Submitted 5 November 2026
- Question
- The quantum random energy model (QREM) puts an independent Gaussian energy of variance \(n\) on each of the \(2^n\) computational-basis states and adds a transverse field. In its spin-glass phase, how long does it take to thermalise when weakly coupled to a bath through single-qubit Pauli operators? Lower bounds on mixing times for noncommuting random Hamiltonians were listed as open, because their eigenbasis, and hence the Davies jump operators, is not explicitly known.
- Result
- For every \(\beta>\beta_c=\sqrt{2\log2}\) and every field \(0\le\Gamma<\Gamma_c(\beta)\), where \(e^{\beta\beta_c}=2\cosh(\beta\Gamma_c)\), the Davies mixing time satisfies \(\liminf_n\frac1n\log T_{\rm mix}\ge c_{\rm mix}>0\) almost surely. This holds for any detailed-balance rates whose maximum grows subexponentially, with or without dephasing terms, and without assuming primitivity.
Methods A three-set flux bound for Davies generators; Localisation turns Hamming distance into suppressed jump rates
Read the full entry →Quantum computing · Theory
Provable circuit-level thresholds for non-abelian topological phases
arXiv:2611.08488v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Abelian topological codes such as the toric code have shallow syndrome circuits and decoders with proven thresholds. Non-abelian phases could offer more powerful logical gates, but outside a few "solvable" cases (\(D_4\), \(S_3\)) there was no explicit syndrome-extraction circuit and no circuit-level threshold proof. Earlier work on the double-Fibonacci phase gave only numerics under simplified noise. Can every non-chiral 2D topological phase serve as a fault-tolerant memory under realistic noise?
- Result
- For every non-chiral bosonic topological order given by a Turaev–Viro state sum, the paper constructs a local circuit that extracts syndromes and applies corrections. It pairs the circuit with a polynomial-time clustering decoder that runs on the fly. Under local stochastic circuit-level noise with rate below a constant threshold \(\epsilon_*\), the logical error probability decays quasi-stretched-exponentially in the system size \(L\). The paper also sketches how the scheme extends to logical gates built from defects.
Methods Bounded-speed clustering decoder; Hierarchical burst decomposition
Read the full entry →Quantum information · Theory
Asymptotic advantage of quantum one-way and SMP communication for total functions
arXiv:2611.07318v1 ↗PDF ↗Submitted 5 November 2026
- Question
- For partial functions, with a promise on the inputs, quantum one-way communication can be exponentially cheaper than classical. For total functions, defined on every input, the question is how large a gap can be at all. Is there a total Boolean function with a polynomial gap between bounded-error quantum and randomised communication in the one-way and simultaneous-message (SMP) models, with public randomness allowed?
- Result
- Yes. Alice holds \(M\in\mathbb F_2^{d\times d}\) and Bob holds \(u,z\in\mathbb F_2^d\), with input length \(n=d^2+2d\). Let \(F_d(M;u,z)=1\) exactly when \((M+M^{\mathsf T})u=z\) and \(u^{\mathsf T}Mu=0\). Then \(Q^{\parallel}(F_d)\) and \(Q^{\to}(F_d)\) are \(\Theta(\sqrt n)\), while \(R^{\to}(F_d)\) and \(R^{\parallel}(F_d)\) are \(\Theta(n)\). With \(2d\) shared EPR pairs, a classical SMP protocol costs \(O(\sqrt n)\), and any entanglement still leaves \(\Omega(\sqrt n)\).
Methods Testing a quadratic form with one phase state; Self-orthogonal subspaces in a Fourier moment bound
Read the full entry →Foundations of quantum mechanics · Theory
Frustration-freeness is decidable but unprovable
arXiv:2611.07337v1 ↗PDF ↗Submitted 5 November 2026
- Question
- A translation-invariant nearest-neighbour Hamiltonian on an \(L\times L\) square lattice, with positive semidefinite bond terms of zero ground energy, is frustration-free if a single state is annihilated by every term. For one fixed \(L\) this is a finite linear-algebra question. Physics usually wants the answer for every \(L\). Is that question decidable when the local dimension \(d\) is fixed? Fixing \(d\) does not settle it on its own: the spectral-gap problem is undecidable on the same inputs.
- Result
- For each \(d\) there is a single size \(L(d)\), the same for every Hamiltonian, such that frustration-freeness on the \(L(d)\times L(d)\) lattice implies it at every size (Theorem 1), so the problem is decidable for each fixed \(d\). Yet, if ZFC is consistent, there is an explicit Hamiltonian with diagonal, commuting terms that is frustration-free at every size although ZFC cannot prove it (Theorem 3). The two fit together because no algorithm computes a valid cutoff for every \(d\) (Theorem 4); the cutoff grows at least like the busy-beaver function, \(L(am+b)\ge\mathrm{BB}(m)\).
Methods Hilbert's basis theorem turns all system sizes into finitely many; Encoding a consistency proof search in tiles
Read the full entry →Quantum information · Theory
Fidelity Determines the Minimum Error of Quantum Recovery
arXiv:2611.07344v1 ↗PDF ↗Submitted 5 November 2026
- Question
- A recovery after noise can be judged by its worst-input entanglement fidelity \(F\), the probability of passing a test that the state and its entanglement with a reference survived. It can also be judged by its operational error \(D=\tfrac12\|\Phi-\mathrm{id}\|_\diamond\), the largest change in any measurement probability. In general \(1-F\le D\le\sqrt{1-F}\). For a fixed noise channel and encoding, do the two coincide once each is optimised over recoveries? Holdsworth, Singh and Wilde proved equality when encoder and decoder share free randomness, and left the unassisted case open.
- Result
- They coincide. For every finite-dimensional channel \(\Phi\) there is an output unitary \(U\) with \[1-F(\mathrm{Ad}_U\Phi)\le D(\mathrm{Ad}_U\Phi)\le1-F(\Phi)\le D(\Phi),\] so over any family of recoveries closed under final unitaries, including Kraus-rank caps, \(\inf D=1-\sup F\). The unitary is the polar part of the Kraus combination weighted by the worst input's amplitudes. The paper also gives a semidefinite program for the best final unitary when the error is below one half, formulas for recovery with a retained noise record, and robustness bounds. In a three-qubit calibration example the optimal correction has 20.3 percent lower operational error than the recovery that maximises average gate fidelity.
Methods Centring the Kraus operators on the worst-case amplitude; A semidefinite program for the best final unitary
Read the full entry →Foundations of quantum mechanics · Experiment
Quantum trajectory of a spin oscillator, continuous retrodiction beyond the Heisenberg uncertainty relation
arXiv:2611.08104v1 ↗PDF ↗Submitted 5 November 2026
- Question
- The Heisenberg relation \(\Delta x\,\Delta p\ge1/2\) limits how well a state predicts the outcomes of measuring two conjugate observables. It says nothing about guesses of a past measurement made with data from both before and after it. Can continuous monitoring of a macroscopic spin oscillator retrodict \(x\), \(p\) and every rotated quadrature at once with variances below the standard quantum limit, and can this be kept up over long runs?
- Result
- In a paraffin-coated \(^{87}\)Rb vapour cell with about \(5.17\times10^{10}\) atoms, alternating stroboscopic QND measurements of \(\hat x_A\) and \(\hat p_A\) at rate \(\kappa^2\eta=2\pi\times1002\) Hz were analysed forwards, with the state \(\rho(t)\), and backwards, with the effect matrix \(E(t)\). Prediction alone gave variances 0.88 dB above the standard quantum limit. Combining past and future data gave both variances \(1.01\pm0.15\) dB below it, so \(\Delta x\,\Delta p\) beat the Heisenberg value, and this held over 1.4 hours. Rotating the verification phase gave sub-SQL retrodicted variances for every quadrature, \(0.388\pm0.025\) on average against 0.5.
Methods Combining a forward state with a backward effect; Alternating QND measurements to watch both quadratures
Read the full entry →Quantum computing · Theory
Quantum Advantage with Sign-Free Proofs: An Oracle Separation between StoqMA and MA
arXiv:2611.08180v1 ↗PDF ↗Submitted 5 November 2026
- Question
- In \(\mathsf{StoqMA}\) the verifier receives a quantum witness, uses ancillas in \(|0\rangle\) and \(|+\rangle\), applies only classical reversible gates (X, CNOT, Toffoli) and makes one Hadamard-basis measurement. The class sits between \(\mathsf{MA}\) and \(\mathsf{AM}\), and if it admitted error reduction it would equal \(\mathsf{MA}\). Its complete problems concern stoquastic, sign-problem-free Hamiltonians, where quantum Monte Carlo often works. Does this nearly classical verifier beat every classical \(\mathsf{MA}\) verifier, at least relative to an oracle?
- Result
- Yes. There is a classical XOR oracle \(\mathcal O\) with \(\mathsf{StoqMA}^{\mathcal O}\ne\mathsf{MA}^{\mathcal O}\) (Theorem 1.1). The separating problem asks whether a sparse, high-girth graph on \(2^m\) vertices, given by a randomly relabelled adjacency-list oracle, has top eigenvalue at least \(n\) or at most \(4\sqrt n\). The verifier receives the Perron eigenvector and runs a Hadamard test that accepts with probability \(1/2+\langle\psi|A|\psi\rangle/(2d)\). That is at least \(3/4\) for the YES graph and at most \(1/2+1/\sqrt n\) for every NO graph. No \(\mathsf{MA}\) verifier with a polynomial witness and polynomially many queries can do this.
Methods A Hadamard test built from a permutation; Degeneracy caps the top eigenvalue
Read the full entry →Quantum computing · Theory
Polynomial-time classical simulation of boson and fermion sampling under thermal loss
arXiv:2611.08444v1 ↗PDF ↗Submitted 5 November 2026
- Question
- Photonic sampling experiments lose a constant fraction of their particles. Does a fixed loss rate already make Haar-random boson or fermion sampling classically easy, without assuming that loss grows with system size, that outputs are dilute, or that circuits are shallow? Earlier simulation results each needed one of those extra conditions.
- Result
- For Fock-state boson sampling, Gaussian boson sampling with fixed uniform squeezing and fermion sampling with four-mode magic inputs, under thermal loss at any fixed transmissivity \(\eta<1\) (pure loss included), there is a classical sampler with error \(\varepsilon\) in total variation, with probability \(1-\delta\) over Haar-random interferometers, in time polynomial in \(m\), \(1/\varepsilon\) and \(1/\delta\) (Theorem III.1). If the ideal output is only polynomially flat, \(\chi^2(\rho_U\|\tau)\le m^{O(1)}\), the time is \((m/\varepsilon)^{O(\log(m/\varepsilon))}\) for any interferometer. It becomes polynomial when loss acts after each of \(\Omega(\log m)\) layers. Near full input filling, the noisy output is close to one fixed distribution, whatever the interferometer.
Methods Loss damps high-degree correlations; From a signed approximation to samples
Read the full entry →Quantum computing · Theory
Algorithmic Wave-Particle Duality: Pathfinding in Welded Trees is Hard
arXiv:2611.05912v1 ↗PDF ↗Submitted 4 November 2026
- Question
- In the welded trees problem, two binary trees of height \(n\) are joined at their leaves by a random cycle, vertices carry random labels, and an algorithm starts at one root. A quantum walk reaches the other root in polynomial time, whereas classical algorithms need exponentially many queries. The walk never records a route, and recording one destroys its interference. Can some other quantum algorithm efficiently output an entrance–exit path? The question had been open since the original paper on the problem.
- Result
- No. Under a distribution over welded trees graphs with a single-cycle weld, any \(q\)-query algorithm outputs an entrance–exit path with probability \[O\Bigl(\frac{q}{2^{n/3}}+\frac{n\,q^3}{2^n}\Bigr),\] so \(\tilde\Omega(2^{n/3})\) queries are needed. This is tight up to factors polynomial in \(n\): find the exit with the walk, then use collision finding to join a root-to-leaf path from each side in \(O(n\,2^{n/3})\) queries.
Methods A good space of records that cannot contain a path; Averaging a collision probability over where the walker is
Read the full entry →Quantum information · Theory
Norm Bounds on Sums of Positive Operators with Applications to Monogamy Games and Quantum Key Distribution
arXiv:2611.05943v1 ↗PDF ↗Submitted 4 November 2026
- Question
- In the BB84 monogamy game, Alice measures \(n\) qubits in random bases, and two separated players, Bob and Charlie, must each guess her outcome string. Perfect guessing has optimal probability \((\cos^2\tfrac\pi8)^n\). If Bob may make \(\beta n\) errors and Charlie \(\gamma n\), for which \((\beta,\gamma)\) does the winning probability still decay exponentially? The existing bound certified decay only up to about 1.53% symmetric error, and the same weakness limited the one-sided device-independent QKD rate built on it.
- Result
- The winning probability decays exponentially if \((1-2\beta)^2+(1-2\gamma)^2>1\), tends to one exponentially fast under the reverse strict inequality, and stays bounded away from zero on the circle itself. The symmetric threshold is \(\sin^2\tfrac\pi8\approx14.64\%\). For one-sided device-independent BB84, where Bob may make an arbitrary joint measurement depending on the whole basis string, every key rate \(0<R<1-2h_2(\gamma)\) is achievable, which is the standard BB84 rate with its 11% noise threshold.
Methods Operator-norm bound via matrix approximation; From a circle of overlaps to sharp thresholds and key rates
Read the full entry →Quantum information · Theory
Equivalence of Correlated Catalytic and Marginal Asymptotic Transformations in Quantum Resource Theories
arXiv:2611.06573v1 ↗PDF ↗Submitted 4 November 2026
- Question
- In correlated catalysis, an auxiliary system helps convert \(\rho\) into (approximately) \(\sigma\), and is returned with exactly its original marginal, though it may end up correlated with the system. A catalyst built from many copies turns any marginal asymptotic conversion at rate one into a correlated-catalytic one. Does the converse hold? In particular, can a correlated catalyst make an undistillable entangled state distillable under LOCC?
- Result
- In every resource theory that allows classical control and processing, permutations, full-rank free states and free informationally complete measurements, \(\rho\) converts to \(\sigma\) by correlated catalysis if and only if the marginal asymptotic rate \(R_{\rm m}(\rho\to\sigma)\) is at least one. Under LOCC, correlated catalysts cannot increase distillable entanglement or distillable key, cannot activate bound entanglement, and cannot raise the two-way private capacity of a finite-dimensional channel.
Methods The cyclic catalyst; Merging of opinions replaces the catalyst
Read the full entry →Quantum computing · Theory
A Quantum Lower Bound for Triangle Finding
arXiv:2611.06751v1 ↗PDF ↗Submitted 4 November 2026
- Question
- Given the adjacency matrix of an \(N\)-vertex graph, how many quantum queries are needed to find a triangle? Upper bounds fell from Grover's \(O(N^{3/2})\) to \(O(N^{5/4})\), but the only lower bound was the \(\Omega(N)\) inherited from unstructured search. Positive-weight adversary methods cannot beat \(O(N)\) here, because a triangle certificate has only three edges.
- Result
- Triangle finding needs \(\Omega(N^{13/12})\) quantum queries, the first superlinear lower bound. The same bound holds for triangle detection and for detecting any fixed connected non-bipartite subgraph. For sparse graphs with \(\bar m\) edges in the range \(N\log N\lesssim\bar m\lesssim N^{3/2}\) the bound \(\Omega(N^{5/6}\bar m^{1/6})\) is tight up to polylogarithmic factors.
Methods The four-input map; Soft averaging over vertex stars
Read the full entry →Foundations of quantum mechanics · Theory (computer-assisted proof)
Using topology to reveal all mutually unbiased bases in dimension six
arXiv:2611.06917v1 ↗PDF ↗Submitted 4 November 2026
- Question
- Two orthonormal bases of \(\mathbb C^d\) are mutually unbiased when every overlap satisfies \(|\langle a_i|b_j\rangle|^2=1/d\): certainty in one basis gives no information about the other. At most \(d+1\) such bases exist, and the bound is reached in every prime-power dimension. Six is the first other dimension. Qubit and qutrit bases give three mutually unbiased bases there, and in 1991 Zauner conjectured that no fourth exists. Which sets exist at all had remained open.
- Result
- All sets of mutually unbiased bases in \(\mathbb C^6\) are classified up to equivalence. Every pair comes from Tao's matrix, from the Fourier matrix \(F_6\), or from a completion \(H_+(\theta)\) built from four phases. Every triple belongs to one known two-parameter family or is the isolated Fourier triple. Neither kind of triple extends, so no four bases exist, \(N(6)=3\). A second test on the same cover rules out quartets directly.
Methods Connectedness turns a finite cover into a global proof; An invariant that separates the two completions
Read the full entry →Foundations of quantum mechanics · Theory (four-qubit bound analytic; seven-qubit bounds computer-assisted)
The most entangled states of four and seven qubits
arXiv:2611.05757v1 ↗PDF ↗Submitted 3 November 2026
- Question
- No pure state of four or seven qubits is maximally entangled across every balanced cut, because absolutely maximally entangled states do not exist at those sizes. How entangled can such a state be on average over its balanced cuts? For four qubits, Higuchi and Sudbery conjectured in 2000 that their state \(M_4\) maximises the mean entropy of the three \(2|2\) cuts.
- Result
- The Higuchi–Sudbery conjecture holds: every four-qubit pure state has mean \(2|2\) entropy at most \(1+\tfrac12\log_23\approx1.792\) bits, with equality only on the local-unitary orbits of \(M_4\) and its complex conjugate. For seven qubits, the mean purity of the 35 cuts of type \(3|4\) is at least \(121/917\) and the mean entropy is at most \(2.965356029\ldots\) bits. Each bound has a unique optimiser up to local unitaries and qubit permutations, and the two optimisers are different members of one icosahedral family.
Methods Moment bounds as positive multi-copy identities; A polynomial majorant that touches at the optimiser's spectrum
Read the full entry →Quantum information · Theory
On Random Purifications of Isometries and Channels
arXiv:2611.04573v1 ↗PDF ↗Submitted 3 November 2026
- Question
- The random purification channel turns copies of a mixed state into copies of a random purification, and has driven recent results in learning and cryptography. Tang, Wright and Zhandry asked whether the same trick lifts queries one level up the hierarchy of maps: can queries to an isometry simulate queries to a random unitary completion, and can queries to a channel simulate queries to a random isometry dilation?
- Result
- The first holds approximately and the second fails badly. An efficient, stateful simulator makes one forward query to an isometry \(V:N\to M\) per call and emulates \(T\) queries to a Haar-random completion with trace-distance error \(O(T\sqrt{N/(M-T)})\). In contrast, two channel ensembles on dimension \(D\) can be told apart perfectly with two queries to any dilation, or with one quantum switch, while \(q\) channel queries give advantage only \(O(q^{3/2}/\sqrt D)\).
Methods Symmetric versus antisymmetric environments; Completing an isometry with a Haar oracle on the whole space
Read the full entry →Quantum computing · Experiment
Autonomous cooling of Kerr-cat qubits to minutes-long bit-flip times
arXiv:2611.04868v1 ↗PDF ↗Submitted 3 November 2026
- Question
- Cat qubits store a bit in two opposite coherent states of an oscillator. Bit flips are then suppressed exponentially in the photon number, which makes noise strongly biased and error correction cheaper. Kerr cats, which are confined by a driven double-well potential, allow fast gates, but excitations inside the wells cause hopping between them, and their bit-flip times had stayed at milliseconds. Can the excitations be removed without new drives or circuit elements?
- Result
- Yes. The three-wave interaction that produces the squeezing drive also couples excitations inside a well to the lossy readout resonator and Purcell filter. When the frequencies match, it drains the excitations. The bit-flip time grows by a factor of \(1.82\pm0.06\) per photon, from 52 µs at \(\bar n=7.4\) to \(448\pm57\) s at \(\bar n=33.8\). Fast \(Z\) gates leave the bit-flip time unchanged, and each readout flips the qubit with probability \((5\pm1)\times10^{-7}\).
Methods Why the confining interaction also cools; Reading a long lifetime from counted jumps
Read the full entry →Quantum information · Theory
Simple proof of conditions requiring maximal entanglement for local state verification and discrimination
arXiv:2611.05317v1 ↗PDF ↗Submitted 3 November 2026
- Question
- Two parties sharing an unknown state want to verify, with certainty and using only local operations and classical communication, whether it is a given entangled \(|\varphi\rangle\). This needs an entangled resource \(|\tau\rangle\). It was known that the resource needs Schmidt rank at least that of \(|\varphi\rangle\), and that at equal rank it must be maximally entangled, but the second fact had only an algebraic-geometry proof. Is there a direct argument, and what does it imply for distinguishing bases?
- Result
- A self-contained linear-algebra proof of both statements, valid even for separable measurements. As a consequence, among resources of local dimension at most \(d\), perfectly distinguishing a basis of \(\mathbb C^d\otimes\mathbb C^d\) that contains one full-Schmidt-rank state requires, and is achieved by, a maximally entangled state of \(\mathbb C^d\otimes\mathbb C^d\). This holds for almost every basis, however weakly entangled its states are.
Methods Counting product vectors for the Schmidt-rank bound; A trace identity that forces equal Schmidt coefficients
Read the full entry →Quantum computing · Theory
Breaking the quantum barriers for Graph Collision
arXiv:2611.05356v1 ↗PDF ↗Submitted 3 November 2026
- Question
- In graph collision, a graph on \(n\) vertices is known in advance, some vertices are marked, and the task is to decide with as few queries as possible whether some edge has both endpoints marked. It is a subroutine for triangle finding. The best quantum algorithm for arbitrary graphs had used \(O(n^{2/3})\) queries since 2005, the lower bound was \(\Omega(\sqrt n)\), and some had conjectured that \(n^{2/3}\) was optimal.
- Result
- The conjecture is false. A first algorithm uses \(\tilde O(n^{92/139})\approx n^{0.662}\) queries and a refined one uses \(\tilde O(n^{11/17})\approx n^{0.647}\). The same bound applies to any Boolean function whose positive inputs have certificates of size two, provided the alphabet is small. In the other direction, an adversary matrix gives \(\Omega(\sqrt{n\log n})\) for a points-and-lines graph, beating the \(\sqrt n\) barrier for positive-weight adversaries.
Methods A least-squares estimate checked against the unknown truth; Balancing the exponents
Read the full entry →Foundations of quantum mechanics · Experiment
Analog quantum simulation of paraparticle statistics
arXiv:2611.03908v1 ↗PDF ↗Submitted 2 November 2026
- Question
- Every particle we know is a boson or a fermion, and older proposals for other statistics in three dimensions turned out to be bosons or fermions with a hidden local label. Wang and Hazzard recently proposed R-paraparticles, whose internal "colour" is a nonlocal property of the many-body state and changes under exchange by a matrix rather than a sign. Can such statistics be produced and seen in a laboratory system?
- Result
- On a 16-transmon lattice, the authors emulate a two-colour (\(m=2\)) paraparticle chain of up to four sites. Exchanging two paraparticles gives a phase of \((1.00\pm0.01)\pi\). Two paraparticles meeting at a 50:50 beamsplitter antibunch whatever their colours. And a single site thermalised against a 14-qubit bath reaches the occupation \(2x/(1+2x)\), which is neither Bose–Einstein nor Fermi–Dirac.
Methods Reading an exchange phase from free evolution; Thermal occupation by counting microstates
Read the full entry →Foundations of quantum mechanics · Theory
Tight Quasiprobabilistic Entropic Uncertainty Relations for Discrete Quantum Systems
arXiv:2611.04009v1 ↗PDF ↗Submitted 2 November 2026
- Question
- The Wehrl–Lieb theorem says coherent states minimise the entropy of the Husimi function. The analogous claim for the Wigner function, that pure Gaussian states minimise the Wigner entropy among states with a positive Wigner function, has been disproved. Does the claim hold for the discrete quasiprobabilities used in quantum information, where some positive states are mixed and extremal?
- Result
- Yes, for Kirkwood–Dirac distributions built on mutually unbiased bases and for Gross–Wigner distributions of odd-dimensional qudits. For every state whose distribution has a nonnegative real part, \[H(A)+H(B)\ge H^{\mathrm{MH}}\ge-\ln\mathrm{Tr}\rho^2+\ln d\ge\ln d,\] and the last bound is reached only on pure positive states. For Kirkwood–Dirac distributions, states with large nonpositivity (mana) must also have large Rényi-½ uncertainty.
Methods Entropy from purity through Jensen's inequality; Nonpositivity bounded by Born-marginal uncertainty
Read the full entry →Quantum computing · Theory
Logarithmic Bias of Zero-Noise Extrapolation under 1/f Noise
arXiv:2611.02444v1 ↗PDF ↗Submitted 2 November 2026
- Question
- Zero-noise extrapolation amplifies noise, for example by folding a circuit into \(U(U^\dagger U)^n\), and fits the measured values to extrapolate to zero noise. The fit assumes a functional form, usually a polynomial or an exponential. Low-frequency noise with a \(1/f\) spectrum is common in solid-state qubits, and folding samples it at longer and longer delays. What response does that produce, and what does it do to the fit?
- Result
- At second order in the coloured noise, the folded response contains a term \(\theta r^2\ln r\), with \(\theta\) set by the noise amplitude and the circuit's forward and inverse response. Any minimal polynomial Richardson rule leaves a bias \(\theta M\) with \(M>0\), equal to \(2.73\theta\) for the nodes 1, 3, 5. Adding \(r^2\ln r\) to the fitting basis removes this bias at that order, without knowing \(\theta\).
Methods Second differences isolate memory; Moment conditions for unbiased extrapolation
Read the full entry →Quantum computing · Theory
unitaryQIP = unitaryPSPACE
arXiv:2611.02819v1 ↗PDF ↗Submitted 2 November 2026
- Question
- Complexity theory for quantum tasks asks how hard it is to prepare states and apply unitaries, not just to decide languages. For states, interactive proofs with a polynomial-time verifier match polynomial space: stateQIP = statePSPACE. For unitaries, which must act correctly on an unknown input that cannot be copied, the analogous question was open in the worst case.
- Result
- The classes coincide: unitaryQIP = unitaryPSPACE. One direction shows that soundness forces a good prover's acceptance probability to be nearly the same on every input. The other synthesises any polynomial-space unitary in polynomial time with a PSPACE oracle, using a recently announced solution to the unitary synthesis problem, and then supplies the oracle through phase states that a prover helps prepare.
Methods Acceptance rigidity: soundness forbids input-dependent acceptance; Oracle queries from injected phase states
Read the full entry →Quantum information · Theory
Correlated Catalysis Removes the Strong Converse for Entanglement Distillation
arXiv:2611.03148v1 ↗PDF ↗Submitted 2 November 2026
- Question
- Distilling Bell pairs from noisy entangled states above the distillable entanglement \(E_D\) cannot succeed reliably. For pure states and some others, a strong converse holds: the fidelity goes to zero. A correlated catalyst is an entangled auxiliary state that is returned exactly in its marginal, though it may become correlated with the output. Does the strong converse survive when such a catalyst is allowed?
- Result
- No. For every distillable state and every rate \(R\), the best asymptotic fidelity with correlated catalysis is \(\min\{1,E_D/R\}\), even when the output–catalyst correlation must vanish. Keeping a fixed fidelity above \(E_D\) needs a catalyst of \(\Theta(n\log(1/\delta_n))\) qubits per side, where \(\delta_n\) bounds the residual mutual information.
Methods A cyclic bank catalyst that lends copies; Turning Bell fidelity into distillable entanglement
Read the full entry →Foundations of quantum mechanics · Experiment
Taming a macroscopic free mass through continuous quantum measurement
arXiv:2611.03159v1 ↗PDF ↗Submitted 2 November 2026
- Question
- Quantum control of mechanical motion has been shown almost only for oscillators, where a trap supplies a frequency and a ground state to aim for. Many proposed tests of gravity and of collapse models want a heavy free mass instead, and a free particle has no trap and no natural scale. Can a milligram object that is effectively free be localised and purified, and how should that be quantified?
- Result
- A 1 mg suspended rotor, with a torsional period of 15 s, behaves as a free particle on the 26 ms timescale of the measurement. Continuous optical-lever measurement localises its angle, giving conditional states of purity \(1.45\times10^{-4}\) from past data and \(5.8\times10^{-4}\) after smoothing with future data. Expressed as entropic temperatures, these are 1.2 µK and 140 nK.
Methods Measurement as the trap: steady states of a monitored free mass; Checking a conditional state against its smoothed version
Read the full entry →Quantum information · Theory
Quantum channel tomography: optimal bounds in the near-boundary regime
arXiv:2611.03639v1 ↗PDF ↗Submitted 2 November 2026
- Question
- How many queries does it take to learn an unknown channel with input dimension \(d_1\), output dimension \(d_2\) and Kraus rank at most \(r\)? With dilation rate \(\tau=rd_2/d_1\ge1\), the answer was known to scale as \(1/\varepsilon\) (Heisenberg) at \(\tau=1\) and as \(1/\varepsilon^2\) (classical) for \(\tau\ge1+\Omega(1)\). In between, the bounds did not match. How does the transition happen?
- Result
- The answer depends on the error measure. In diamond norm the complexity is \(\Theta(rd_1d_2/\varepsilon^2)\) as soon as \(\tau>1\), so Heisenberg scaling is lost abruptly. In normalised Choi trace norm it is \[\Theta\!\Big(\frac{d_1^2}\varepsilon+\frac{\min\{(\tau-1)d_1^2,(\tau-1)^2d_1^2d_2^2\}}{\varepsilon^2}\Big),\] so the classical part grows gradually with distance from the boundary.
Methods Bounding discrimination by a representation-dimension ratio; Splitting estimation error into the image and its complement
Read the full entry →Foundations of quantum mechanics · Theory
Detection times are not local observables in quantum field theory
arXiv:2611.02135v1 ↗PDF ↗Submitted 1 November 2026
- Question
- Detectors record when they click, and the record sits in a bounded region of spacetime. In algebraic quantum field theory, a measurement is usually taken to be localised in a region when its effects belong to that region's local algebra. Can a detection-time observable be localised in that sense?
- Result
- No. A family of detection-time POVMs that is consistent when the recording is extended, covariant under time translation, and normalised must give zero on any invariant vector. In QFT the vacuum is invariant and, by Reeh–Schlieder, separating for every bounded-region algebra. So every nonzero detection-time effect lies outside every bounded-region local algebra.
Methods A counting argument against invariant vectors; Why vacuum annihilation excludes locality, and what it breaks
Read the full entry →Foundations of quantum mechanics · Theory
Almost-Quantum Correlations Violate Information Causality
arXiv:2610.41444v1 ↗PDF ↗Submitted 30 October 2026
- Question
- Information causality says that \(m\) bits of communication cannot give a receiver more than \(m\) bits about a sender's independent data. It was hoped that this principle might help single out quantum correlations. Almost-quantum correlations were the hard test, because they pass most other proposed principles and numerics suggested they pass this one too. Do they?
- Result
- No. One almost-quantum box and one classical bit violate information causality, and without bound as the number of settings grows. The score exceeds 1 first at \(N=757\,693\) settings per party. The mechanism is a rare but never wrong certificate that vouches for many of the sender's bits at once.
Methods Zero-error certificates: information linear in probability; Building a box from vectors that commute only on the state
Read the full entry →Quantum information · Theory
Bounding Fidelity of Non-Stabilizer States from Local Pauli Measurements
arXiv:2610.41808v1 ↗PDF ↗Submitted 30 October 2026
- Question
- Estimating fidelity to a target state is the standard check on a large prepared state, but direct estimation with local Pauli measurements becomes costly for states with much magic. Hypergraph states are a key example. Often only a rigorous bound is needed. Can it be obtained from cheap measurements, without an exponentially large optimisation?
- Result
- Yes. Measure only low-order stabilizer moments, which have low overhead, and solve a linear program with just \(n+1\) variables for the smallest and largest fidelity compatible with the data. Expected sample cost is \(O(2^K\ln(K/\delta)/\epsilon^2)\) at order \(K\), independent of \(n\), and simulations reach \(n=500\) qubits for hypergraph states.
Methods Symmetry from the choice of measurements; Reading many hypergraph operators from one Pauli setting
Read the full entry →Quantum information · Theory
Channel dichotomies
arXiv:2610.41858v1 ↗PDF ↗Submitted 30 October 2026
- Question
- How many uses of a channel \(W\) can \(n\) uses of a channel \(T\) simulate at a given error? To first order the answer is the capacity ratio. Coding then simulating is known not to be optimal at finite length, since a noisy channel simulates itself exactly. So what is the true second-order correction, in general?
- Result
- With non-signalling assistance and a single dispersion per channel, the best target length is \(rn+(d_\epsilon/C_W)\sqrt n+O(\log n)\), where \(r=C_T/C_W\). The coefficient \(d_\epsilon\) is an optimisation of a difference of Gaussian quantiles, from the sesquinormal law of state dichotomies. At a special error it vanishes, and for matched channels that error is zero.
Methods Gaussian comparison of testing curves; Keeping the noise instead of removing it
Read the full entry →Foundations of quantum mechanics · Theory
No generalised contextuality from the vacuum
arXiv:2610.41964v1 ↗PDF ↗Submitted 30 October 2026
- Question
- Earlier work showed that a detector can harvest Kochen–Specker-type contextuality from a quantum field's vacuum. Contextuality has several inequivalent definitions, however. Can the operational notion due to Spekkens be created the same way, by letting noncontextual detector states interact with the field?
- Result
- In two regimes it cannot. The effective channel on an Unruh–DeWitt detector, with the field traced out, is invertible at finite order in perturbation theory and exactly in the zero-gap limit, including for \(N\) qudits. An invertible channel keeps a noncontextual set of states noncontextual.
Methods Invertible channels preserve noncontextuality; Exact gapless evolution by a terminating Magnus series
Read the full entry →