Optimal choice of state tomography quorum formed by projection operators

TL;DR

This paper explores the optimal selection of measurement projections for quantum state tomography in highly degenerate cases, demonstrating that numerically optimized projectors outperform traditional mutually unbiased bases.

Contribution

It introduces numerically optimized measurement sets for degenerate quantum states, surpassing the performance of standard mutually unbiased bases.

Findings

Optimized projectors significantly outperform MUB-based sets.

Numerical methods improve measurement efficiency in degenerate cases.

Maximal degeneracy requires different measurement strategies.

Abstract

A minimal set of measurement operators for quantum state tomography has in the non-degenerate case ideally eigenbases which are mutually unbiased. This is different for the degenerate case. Here, we consider the situation where the measurement operators are projections on individual pure quantum states. This corresponds to maximal degeneracy. We present numerically optimized sets of projectors and find that they significantly outperform those which are taken from a set of mutually unbiased bases.