Entanglement map · Partial

For which parties and dimensions do AME states exist?

Settled in some cases only.

An AME state is maximally mixed on every reduction to half of its parties or fewer. None exists for seven qubits, and four six-level systems, an open problem until 2021, do have one.

Still unknown

Existence is a case-by-case question across n and d. One 2026 preprint names AME(8,4) as the first remaining open case, assuming the seven-party result below holds.

Connections

• Part of: Multipartite entanglement
• Narrowed by: Seven-party AME states exist exactly when d ≥ 3

Sources

• How entangled can two couples get?. A. Higuchi, A. Sudbery, 2000.
• Absolutely maximally entangled states of seven qubits do not exist. F. Huber, O. Gühne, J. Siewert, 2016.
• Thirty-six entangled officers of Euler: quantum solution to a classically impossible problem. S. A. Rather, A. Burchardt, W. Bruzda, G. Rajchel-Mieldzioć, A. Lakshminarayan, K. Życzkowski, 2021.
• Five open problems in quantum information. P. Horodecki, Ł. Rudnicki, K. Życzkowski, 2020.
• Symmetry-guided constructions of absolutely maximally entangled states in five open cases. S. Bevins, Y. Bidav, et al., 2026.

Checked 2026-10-30.