Entropy, Stochastic Matrices, and Quantum Operations

TL;DR

This paper explores conditions for the saturation of subadditivity inequalities in stochastic matrices, introducing a quantum-inspired relative entropy concept and examining its properties and connections to quantum operations.

Contribution

It introduces a new relative entropy for stochastic matrices inspired by quantum entropy and analyzes its properties and relation to quantum operations.

Findings

Conditions for subadditivity saturation in stochastic matrices

Properties of the new relative entropy concept

Connections between stochastic matrix entropy and quantum operations

Abstract

The goal of the present paper is to derive some conditions on saturation of (strong) subadditivity inequality for the stochastic matrices. The notion of relative entropy of stochastic matrices is introduced by mimicking quantum relative entropy. Some properties of this concept are listed and the connection between the entropy of the stochastic quantum operations and that of stochastic matrices are discussed.