The Quantum Bayes Rule and Generalizations from the Quantum Maximum Entropy Method

TL;DR

This paper derives the Quantum Bayes Rule and its generalizations using the quantum maximum entropy method, linking inferential updating of density matrices to physical and experimental implications in quantum mechanics.

Contribution

It provides a new derivation of the Quantum Bayes Rule via the quantum maximum entropy method and discusses its limitations in quantum measurement processes.

Findings

Derivation of Quantum Bayes Rule from maximum entropy principles

Generalizations of the Quantum Bayes Rule presented

Discussion of measurement limitations in quantum mechanics

Abstract

The recent article "Entropic Updating of Probability and Density Matrices" [1] derives and demonstrates the inferential origins of both the standard and quantum relative entropies in unison. Operationally, the standard and quantum relative entropies are shown to be designed for the purpose of inferentially updating probability distributions and density matrices, respectively, when faced with incomplete information. We call the inferential updating procedure for density matrices the "quantum maximum entropy method". Standard inference techniques in probability theory can be criticized for lacking concrete physical consequences in physics; but here, because we are updating quantum mechanical density matrices, the quantum maximum entropy method has direct physical and experimental consequences. The present article gives a new derivation of the Quantum Bayes Rule, and some generalizations, using the quantum maximum entropy method while discuss some of the limitations the quantum maximum entropy method puts on the measurement process in Quantum Mechanics.