Bayesian Interpretation of Weak Values

TL;DR

This paper presents a Bayesian interpretation of weak values in quantum mechanics, linking them to conditional probabilities and providing a protocol for their experimental determination with minimal disturbance.

Contribution

It introduces a quantum Bayes relation framework for weak values and offers an explicit measurement protocol using a Mach-Zehnder interferometer.

Findings

Derived formulae for weak values from experimental data

Proposed a minimally invasive state tomography method

Established a connection between weak values and Bayesian probabilities

Abstract

The real part of the weak value is identified as the conditional Bayes probability through the quantum analog of the Bayes relation. We present an explicit protocol to get the the weak values in a simple Mach-Zehnder interferometer model and derive the formulae for the weak values in terms of the experimental data consisting of the positions and momenta of detected photons on the basis of the quantum Bayes relation. The formula gives a way of tomography of the initial state almost without disturbing it in the weak coupling limit.