Open Quantum Problem 13: Mutually unbiased bases
Special case in dimension 6: determine the maximal number of mutually unbiased orthonormal bases in ℂ^6.
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Open problems
Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.
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Open Quantum Problem 23: SIC-POVMs
Benchmark open subproblem: existence of a SIC-POVM in dimension 56.
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Open Quantum Problem 35: existence of absolutely maximally entangled pure states
Open benchmark statement: does an AME(8,4) state exist?
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