Maximum a posteriori estimation of quantum states

TL;DR

This paper introduces a Bayesian maximum a posteriori (MAP) estimator for quantum state and process tomography, unifying existing estimators and enabling efficient computation with prior knowledge, including noise correction.

Contribution

It presents the MAP estimator as a unified framework for quantum tomography that incorporates prior knowledge and simplifies computation using convex optimization.

Findings

MAP estimator generalizes existing methods

Enables noise correction in quantum state estimation

Facilitates efficient numerical computation

Abstract

Using a Bayesian methodology, we introduce the maximum a posteriori~(MAP) estimator for quantum state and process tomography. The maximum likelihood, hedged maximum likelihood, maximum likelihood-maximum entropy estimator, and estimators of this general type, can be viewed as special cases of the MAP estimator. The MAP, like the Bayes mean estimator includes prior knowledge, however for cases of interest to tomography can take advantage of convex optimization tools making it numerically easier to compute. We show how the MAP and other Bayesian quantum state estimators can be corrected for noise produced if the quantum state passes through a noisy quantum channel prior to measurement.