Near-optimal quantum tomography: estimators and bounds

TL;DR

This paper establishes tight bounds on the average fidelity in quantum state tomography, introduces online computable bounds, and highlights the Bayesian mean estimator's near-optimal performance across finite-dimensional systems.

Contribution

It provides the first tight, online computable bounds on average fidelity and demonstrates the near-optimality of the Bayesian mean estimator in quantum tomography.

Findings

Bounds are tight for relevant density matrix distributions

Bayesian mean estimator performs close to the bounds

Bounds are applicable to all finite-dimensional quantum systems

Abstract

We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the experiment is running. We show numerically that these bounds are quite tight for relevant distributions of density matrices. We also show that the Bayesian mean estimator is ideal in the sense of performing close to the bound without requiring optimization. Our results hold for all finite dimensional quantum systems.