Conditional Decoupling of Quantum Information

TL;DR

This paper introduces models of conditional decoupling in tripartite quantum systems, demonstrating that the minimal noise rate needed to erase correlations is quantified by the conditional quantum mutual information, thus providing an operational measure.

Contribution

It establishes that the deconstruction and conditional erasure costs are equal to the conditional quantum mutual information, offering a new operational interpretation for this measure.

Findings

Conditional decoupling models are introduced for tripartite states.

The minimal noise rate for correlation erasure equals the conditional quantum mutual information.

Provides an operational interpretation for the conditional quantum mutual information.

Abstract

Insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states. In that spirit, Groisman, Popescu, and Winter [Physical Review A 72, 032317 (2005)] showed that the quantum mutual information $I(A;B)$ quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems $AB$. Here, we investigate correlations in tripartite systems $ABE$. In particular, we are interested in the minimal rate of noise needed to apply to the systems $AE$ in order to erase the correlations between $A$ and $B$ given the information in system $E$, in such a way that there is only negligible disturbance on the marginal $BE$. We present two such models of conditional decoupling, called deconstruction and conditional erasure cost of tripartite states $ABE$. Our main result is that both are equal to the conditional quantum mutual information $I(A;B|E)$ -- establishing it as an operational measure for tripartite quantum correlations.