All Multiparty Quantum States Can Be Made Monogamous

TL;DR

This paper demonstrates that any multiparty quantum state can be rendered monogamous with respect to any quantum correlation measure by applying an appropriate monotonically increasing function, broadening the understanding of quantum correlation sharability.

Contribution

It introduces a general method to convert any quantum correlation measure into a monogamous form for all multiparty states, regardless of purity or dimension.

Findings

All multiparty states can be made monogamous with respect to any measure.

A monotonically increasing function can transform non-monogamous measures into monogamous ones.

The approach applies to all states, measures, and dimensions, including the quantum work deficit.

Abstract

Monogamy of quantum correlation measures puts restrictions on the sharability of quantum correlations in multiparty quantum states. Multiparty quantum states can satisfy or violate monogamy relations with respect to given quantum correlations. We show that all multiparty quantum states can be made monogamous with respect to all measures. More precisely, given any quantum correlation measure that is non-monogamic for a multiparty quantum state, it is always possible to find a monotonically increasing function of the measure that is monogamous for the same state. The statement holds for all quantum states, whether pure or mixed, in all finite dimensions and for an arbitrary number of parties. The monotonically increasing function of the quantum correlation measure satisfies all the properties that is expected for quantum correlations to follow. We illustrate the concepts by considering a thermodynamic measure of quantum correlation, called the quantum work deficit.