Are general quantum correlations monogamous?

TL;DR

This paper investigates the monogamy properties of quantum correlations beyond entanglement, revealing that only entanglement measures are strictly monogamous across all states, while other measures like discord can be monogamous only in specific cases.

Contribution

It proves that monogamous correlation measures must vanish on separable states and shows geometric discord is monogamous for all three-qubit pure states.

Findings

Entanglement measures are uniquely monogamous for all states.

Quantum discord is not generally monogamous, except in specific cases.

Geometric discord satisfies monogamy on all three-qubit pure states.

Abstract

Quantum entanglement and quantum non-locality are known to exhibit monogamy, that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove in general that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.