Private quantum decoupling and secure disposal of information

TL;DR

This paper introduces private quantum decoupling, a method for locally reducing correlations in bipartite quantum states without environmental transfer, revealing quantum features and operational interpretations of ineliminable correlations.

Contribution

It proposes the paradigm of private quantum decoupling, establishes bounds on ineliminable correlations, and links these to entanglement and coherent information.

Findings

Ineliminable correlations satisfy a monogamy constraint in tripartite pure states.

Ineliminable correlations serve as an entanglement measure.

Regularized ineliminable correlations equal the coherent information.

Abstract

Given a bipartite system, correlations between its subsystems can be understood as information that each one carries about the other. In order to give a model-independent description of secure information disposal, we propose the paradigm of private quantum decoupling, corresponding to locally reducing correlations in a given bipartite quantum state without transferring them to the environment. In this framework, the concept of private local randomness naturally arises as a resource, and total correlations get divided into eliminable and ineliminable ones. We prove upper and lower bounds on the amount of ineliminable correlations present in an arbitrary bipartite state, and show that, in tripartite pure states, ineliminable correlations satisfy a monogamy constraint, making apparent their quantum nature. A relation with entanglement theory is provided by showing that ineliminable correlations constitute an entanglement parameter. In the limit of infinitely many copies of the initial state provided, we compute the regularized ineliminable correlations to be measured by the coherent information, which is thus equipped with a new operational interpretation. In particular, our results imply that two subsystems can be privately decoupled if their joint state is separable.