Mutually unbiased bases: common states, completion, and extension obstructions

arXiv:2610.12180 · quant-ph, math-ph, math.CO, math.MP · Submitted 2026-10-08 · Read on arXiv

quant-ph, math-ph, math.CO, math.MP

Submitted: 2026-10-08

Updated: 2026-10-08

Terminology

• Trace — 6× in this paper · explained in 2 episodes
• Consistency — 5× in this paper · explained in 3 episodes
• Verification — 4× in this paper · explained in 2 episodes
• Verifier — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Formal Verification — 1× in this paper · explained in 2 episodes
• Provenance — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes

Sources

• Cyclic p-roots of prime lengths p and related complex Hadamard matrices
• Quantum Integrable Model of an Arrangement of Hyperplanes
• Proudfoot-Speyer degenerations of scattering equations
• Constructing Mutually Unbiased Bases in Dimension Six
• Type-II Matrices and Combinatorial Structures
• More mutually unbiased bases
• Threeparameter complex Hadamard matrices of order 6
• A Criterion for Attaining the Welch Bounds with Applications for Mutually Unbiased Bases
• A two-parameter family of complex Hadamard matrices of order 6 induced by hypocycloids
• A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6
• Mutually unbiased triplets from non-affine families of complex Hadamard matrices in dimension six
• Mutually unbiased bases with free parameters
• Sinkhorn normal form for unitary matrices
• On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six
• Symplectic geometry of unbiasedness and critical points of a potential
• Orthogonal pairs and mutually unbiased bases
• Theory of homotopes in application to mutually unbiased bases, harmonic analysis on graphs and perverse sheaves
• Mutually Unbiased Bases in Composite Dimensions -- A Review
• Incompatible measurements in quantum information science

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