Monogamy of Correlations vs. Monogamy of Entanglement

TL;DR

This paper reviews and extends the understanding of how quantum and non-local correlations can be shared among parties, highlighting their monogamy properties and implications for quantum security.

Contribution

It provides new proofs and results on the shareability of correlations, explores the relationship between quantum entanglement and non-locality, and assesses implications for quantum cryptography.

Findings

Quantum correlations have limited shareability and can be monogamous.

A new, simpler proof of the Toner-Verstraete monogamy inequality is presented.

Sharing non-local correlations relates non-trivially to sharing entangled states.

Abstract

A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results as well as present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell's theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, although, and importantly, it is stressed that not all non-local correlations are monogamous.