Conditional Mutual Information and Quantum Steering

TL;DR

This paper introduces an information-theoretic measure called intrinsic steerability based on conditional mutual information to quantify quantum steering, linking it to resource theory and operational tasks.

Contribution

It proposes a new quantifier for quantum steering using conditional mutual information and explores its properties and operational significance.

Findings

Intrinsic steerability quantifies deviation from local hidden-state models.

The measure satisfies desirable monotonic properties.

It has an operational interpretation as classical communication cost.

Abstract

Quantum steering has recently been formalized in the framework of a resource theory of steering, and several quantifiers have already been introduced. Here, we propose an information-theoretic quantifier for steering called intrinsic steerability, which uses conditional mutual information to measure the deviation of a given assemblage from one having a local hidden-state model. We thus relate conditional mutual information to quantum steering and introduce monotones that satisfy certain desirable properties. The idea behind the quantifier is to suppress the correlations that can be explained by an inaccessible quantum system and then quantify the remaining intrinsic correlations. A variant of the intrinsic steerability finds operational meaning as the classical communication cost of sending the measurement choice and outcome to an eavesdropper who possesses a purifying system of the underlying bipartite quantum state that is being measured.