Operator system characterizations of SIC-POVMs and mutually unbiased bases

2024/10/01 by Travis B. Russell, Russell, Travis B.
Computer Science · Engineering · #46L07 #47L25 #81P55 #Contact Mechanics and Variational Inequalities #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Quantum Physics (quant-ph) #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2410.01119

openalex publication_date 2024/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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 d²-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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