The Quantum Reverse Shannon Theorem based on One-Shot Information Theory

The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel's entanglement assisted classical capacity. In this paper, we provide a new proof of this theorem, which has previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof has a clear structure being based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channels.Comment: 30 pages, 4 figures, published versio

Private quantum decoupling and secure disposal of information

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.Comment: Child of 0807.3594 v2: minor changes v3: presentation improved, one figure added v4: extended version with a lot of discussions and examples v5: published versio

Why should we care about quantum discord?

Entanglement is a central feature of quantum theory. Mathematical properties and physical applications of pure state entanglement make it a template to study quantum correlations. However, an extension of entanglement measures to mixed states in terms of separability does not always correspond to all the operational aspects. Quantum discord measures allow an alternative way to extend the idea of quantum correlations to mixed states. In many cases these extensions are motivated by physical scenarios and quantum information protocols. In this chapter we discuss several settings involving correlated quantum systems, ranging from distributed gates to detectors testing quantum fields. In each setting we show how entanglement fails to capture the relevant features of the correlated system, and discuss the role of discord as a possible alternative.Comment: Written for "Lectures on general quantum correlations and their applications