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arXiv · 2503.14752

Triplets of Mutually Unbiased Bases

Máte Matolcsi·Ákos K. Matszangosz·Dániel Varga·Mihály Weiner
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Abstract

We initiate a systematic study of triplets of mutually unbiased bases (MUBs). We show that in $\mathbb{C}^d$ each MUB-triplet is characterized by a $d\times d\times d$ object that we call a Hadamard cube. We describe the basic properties of Hadamard cubes, and show how an MUB-triplet can be reconstructed from such a cube, up to unitary equivalence. We also present an algebraic identity which is conjectured to hold for all MUB-triplets in dimension 6. If true, it would imply the long-standing conjecture of Zauner that the maximum number of MUBs in dimension 6 is three.

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Máte Matolcsi, Ákos K. Matszangosz, Dániel Varga, Mihály Weiner. 2025-07-19. Triplets of Mutually Unbiased Bases. https://arxiv.org/abs/2503.14752

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