Communication capacity of mixed quantum t designs

TL;DR

This paper introduces mixed quantum t-designs, extending projective t-designs to arbitrary ranks, and analyzes their classical communication capacities, providing bounds and explicit calculations for various important quantum measurements.

Contribution

It defines mixed quantum t-designs and derives bounds and exact capacities for their associated measurements, advancing understanding of quantum measurement indistinguishability.

Findings

Derived upper bounds on communication capacity for t in [1,5]

Computed capacities for depolarized SIC and MUB measurements

Analyzed capacities of special measurements like Hoggar SIC and anti-SIC

Abstract

We operationally introduce mixed quantum t-designs as the most general arbitrary-rank extension of projective quantum t-designs which preserves indistinguishability from the uniform distribution for t copies. First, we derive upper bounds on the classical communication capacity of any mixed t-design measurement for t in [1,5]. Second, we explicitly compute the classical communication capacity of several mixed t-design measurements, including the depolarized version of any qubit and qutrit symmetric, informationally complete (SIC) measurement and complete mutually unbiased bases, the qubit icosahedral measurement, the Hoggar SIC measurement, any anti-SIC (where each element is proportional to the projector on the subspace orthogonal to one of the elements of the original SIC), and the uniform distribution over pure effects.