Conditions for Monogamy of Quantum Discord: Greenberger-Horne-Zeilinger versus W states

TL;DR

This paper investigates the monogamy properties of quantum discord in multipartite states, identifying conditions under which it obeys monogamy, and finds that GHZ states satisfy monogamy while W states do not.

Contribution

It extends the concept of monogamy to quantum discord, providing necessary and sufficient conditions for monogamy in arbitrary states, and compares GHZ and W states.

Findings

GHZ states obey monogamy of quantum discord

W states violate monogamy of quantum discord

Conditions for monogamy depend on interaction information

Abstract

Quantum correlations are expected to respect all the conditions required for them to be good measures of quantumness in the bipartite scenario. In a multipartite setting, sharing entanglement between several parties is restricted by the monogamy of entanglement. We take over the concept of monogamy to an information-theoretic quantum correlation measure, and find that it violates monogamy in general. Using the notion of interaction information, we identify necessary and sufficient conditions for the measure to obey monogamy, for arbitrary pure and mixed quantum states. We show that while three-qubit generalized Greenberger-Horne-Zeilinger states follow monogamy, generalized W states do not.