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arXiv · 2410.01119

Operator system characterizations of SIC-POVMs and mutually unbiased bases

Travis B. Russell
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Abstract

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.

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Travis B. Russell. 2024-10-01. Operator system characterizations of SIC-POVMs and mutually unbiased bases. https://doi.org/10.1007/s00023-025-01633-4

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