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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23997 |
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| _version_ | 1866910110679302144 |
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| author | McNulty, Daniel Weigert, Stefan |
| author_facet | McNulty, Daniel Weigert, Stefan |
| contents | Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a foundational context and for applications. To date, it remains unknown if complete sets of mutually unbiased bases exist in Hilbert spaces of dimensions different from a prime power, i.e. in composite dimensions such as six or ten. Fourteen mathematically equivalent formulations of the existence problem are presented. We comprehensively summarise analytic, computer-aided and numerical results relevant to the case of composite dimensions. Known modifications of the existence problem are reviewed and potential solution strategies are outlined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mutually Unbiased Bases in Composite Dimensions -- A Review McNulty, Daniel Weigert, Stefan Quantum Physics Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a foundational context and for applications. To date, it remains unknown if complete sets of mutually unbiased bases exist in Hilbert spaces of dimensions different from a prime power, i.e. in composite dimensions such as six or ten. Fourteen mathematically equivalent formulations of the existence problem are presented. We comprehensively summarise analytic, computer-aided and numerical results relevant to the case of composite dimensions. Known modifications of the existence problem are reviewed and potential solution strategies are outlined. |
| title | Mutually Unbiased Bases in Composite Dimensions -- A Review |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.23997 |