Operator system characterizations of SIC-POVMs and mutually unbiased bases

TL;DR

This paper establishes a new operator system framework to characterize the existence of SIC-POVMs and mutually unbiased bases in quantum information theory, providing constructive methods and theoretical insights.

Contribution

It introduces an operator system approach to characterize SIC-POVMs and mutually unbiased bases, offering new construction techniques and theoretical equivalences.

Findings

Existence of SIC-POVMs is equivalent to certain operator systems.

Constructive method for building these operator systems.

Successful initial step in the construction process.

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.