Quantum Entanglement and Conditional Information Transmission

TL;DR

This paper introduces a new quantum entanglement measure based on conditional information transmission, which aligns with Entanglement of Formation for pure bipartite states and extends naturally to multi-partite systems.

Contribution

The paper proposes a novel entanglement measure defined via conditional information transmission in Quantum Bayesian Nets, with properties and connections to data processing inequalities.

Findings

Measure equals Entanglement of Formation for pure bipartite states

Generalizes to n-partite systems with desirable properties

Provides a new upper bound for classical mutual information

Abstract

We propose a new measure of quantum entanglement. Our measure is defined in terms of conditional information transmission for a Quantum Bayesian Net. We show that our measure is identically equal to the Entanglement of Formation in the case of a bipartite (two listener) system occupying a pure state. In the case of mixed states, the relationship between these two measures is not known yet. We discuss some properties of our measure. Our measure can be easily and naturally generalized to handle n-partite (n-listener) systems. It is non-negative for any n. It vanishes for conditionally separable states with n listeners. It is symmetric under permutations of the n listeners. It decreases if listeners are merged, pruned or removed. Most promising of all, it is intimately connected with the Data Processing Inequalities. We also find a new upper bound for classical mutual information which is of interest in its own right.