Entropic Updating of Probability and Density Matrices

TL;DR

This paper develops a quantum maximum entropy method for updating density matrices based on relative entropy, deriving both classical and quantum entropies from shared inferential principles to improve inference in quantum mechanics.

Contribution

It introduces a unified derivation of classical and quantum entropies from inferential criteria, enabling a quantum maximum entropy approach for density matrix inference.

Findings

Derived classical relative entropy and quantum Umegaki entropy from common principles

Formulated a quantum maximum entropy method for density matrix inference

Provides a unified framework for entropy-based inference in quantum mechanics

Abstract

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information in Quantum Mechanics.