Operator system characterizations of SIC-POVMs and mutually unbiased bases
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909888380141568 |
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| author | Russell, Travis B. |
| author_facet | Russell, Travis B. |
| contents | We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension $d$ if and only if there exists a $d^2$-dimensional operator system satisfying certain order-theoretic conditions. We also describe a method of constructing such an operator system and demonstrate that the first step of this construction can be carried out successfully. We obtain analogous results for the existence of $d+1$ mutually unbiased bases in a given dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator system characterizations of SIC-POVMs and mutually unbiased bases Russell, Travis B. Quantum Physics Operator Algebras 46L07, 47L25, 81P55 We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension $d$ if and only if there exists a $d^2$-dimensional operator system satisfying certain order-theoretic conditions. We also describe a method of constructing such an operator system and demonstrate that the first step of this construction can be carried out successfully. We obtain analogous results for the existence of $d+1$ mutually unbiased bases in a given dimension. |
| title | Operator system characterizations of SIC-POVMs and mutually unbiased bases |
| topic | Quantum Physics Operator Algebras 46L07, 47L25, 81P55 |
| url | https://arxiv.org/abs/2410.01119 |