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

All Multiparty Quantum States Can Be Made Monogamous