Triplets of Mutually Unbiased Bases
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913949232922624 |
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| author | Matolcsi, Máte Matszangosz, Ákos K. Varga, Dániel Weiner, Mihály |
| author_facet | Matolcsi, Máte Matszangosz, Ákos K. Varga, Dániel Weiner, Mihály |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14752 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Triplets of Mutually Unbiased Bases Matolcsi, Máte Matszangosz, Ákos K. Varga, Dániel Weiner, Mihály Combinatorics 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. |
| title | Triplets of Mutually Unbiased Bases |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.14752 |