A Bayesian quasi-probability approach to inferring the past of quantum observables

TL;DR

This paper introduces a Bayesian quasi-probability method using Wigner representations to infer the history of quantum observables, compatible with quantum logic and capable of handling complex quantum features.

Contribution

It presents a novel Bayesian approach with Wigner quasi-probability to infer quantum observable histories, accommodating incompatible observables and quantum phenomena.

Findings

Compatible with quantum logic for large subclasses of systems

Handles incompatible observables and quantum features

Provides a consistent inference framework for quantum histories

Abstract

I describe a method of inferring the past of quantum observables given the initial state and the subsequent measurement results using Wigner quasi-probability representations. The method is proved to be compatible with logic for large subclasses of quantum systems, including those that involve incompatible observables and can still exhibit some quantum features, such as the uncertainty relation, measurement backaction, and entanglement.