Non-monogamy of quantum discord and upper bounds for quantum correlation

TL;DR

This paper explores the monogamy properties of quantum discord, establishes its relation to quantum mutual information and entanglement of formation, and discusses bounds and limitations of quantum correlations in tripartite states.

Contribution

It demonstrates the equivalence between monogamy inequality of quantum discord and an inequality involving mutual information and entanglement of formation, revealing conditions for monogamy and polygamy.

Findings

Quantum discord can be both monogamous and polygamous.

An inequality between quantum mutual information and entanglement of formation is key to monogamy.

Previous conjectured upper bounds of quantum correlation are invalid.

Abstract

We consider a monogamy inequality of quantum discord in a pure tripartite state and show that it is equivalent to an inequality between quantum mutual information and entanglement of formation of two parties. Since this inequality does not hold for arbitrary bipartite states, quantum discord can generally be both monogamous and polygamous. We also carry out numerical calculations for some special states. The upper bounds of quantum discord and classical correlation are also discussed and we give physical analysis on the invalidness of a previous conjectured upper bound of quantum correlation. Our results provide new insights for further understanding of distributions of quantum correlations.