Monogamy properties of quantum and classical correlations

TL;DR

This paper explores the monogamy properties of quantum and classical correlations, revealing that quantum discord in pure states aligns with entanglement of formation and analyzing monogamy in three-qubit and rank-2 states.

Contribution

It establishes the equivalence of quantum discord and entanglement of formation for pure states and analyzes monogamy properties in specific quantum states.

Findings

Quantum discord in pure states equals entanglement of formation.

No monogamy in W states for three-qubit pure states.

Discord and classical correlations are bounded by single-qubit entropies in rank-2 states.

Abstract

In contrast with entanglement, as measured by concurrence, in general, quantum discord does not possess the property of monogamy, that is, there is no tradeoff between the quantum discord shared by a pair of subsystems and the quantum discord that both of them can share with a third party. Here, we show that, as far as monogamy is considered, quantum discord of pure states is equivalent to the entanglement of formation. This result allows one to analytically prove that none of the pure three-qubit states belonging to the subclass of W states is monogamous. A suitable physical interpretation of the meaning of the correlation information as a quantifier of monogamy for the total information is also given. Finally, we prove that, for rank 2 two-qubit states, discord and classical correlations are bounded from above by single-qubit von Neumann entropies.