Practical Bayesian Tomography

TL;DR

This paper advances Bayesian quantum tomography by making it computationally feasible, introducing informative priors, and enabling tracking of time-dependent quantum states, supported by practical code and visualizations.

Contribution

It presents a comprehensive solution addressing computational, prior, and dynamic tracking challenges in Bayesian quantum tomography.

Findings

Achieved practical computation of Bayesian estimators for quantum states and channels.

Introduced the first informative priors for quantum states and channels.

Developed a method for tracking time-dependent quantum states and their drift.

Abstract

In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Husz\'ar and Houlsby and by Ferrie, to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first priors on quantum states and channels that allow for including useful experimental insight. Finally, we develop a method that allows tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.