What does monogamy in higher powers of a correlation measure mean?

TL;DR

This paper investigates whether raising quantum correlation measures to higher powers enforces monogamy in multiparty quantum states, finding that such approaches are generally ineffective and can be misleading.

Contribution

It demonstrates that higher powers of quantum correlation measures do not reliably establish monogamy, challenging previous assumptions and providing counterexamples.

Findings

Higher powers of quantum deficit satisfy monogamy inequality for symmetric 3-qubit states.

Higher powers of classical mutual information do not necessarily imply restricted shareability.

Raising correlation measures to higher powers is not a reliable method to prove monogamy in multiparty states.

Abstract

We examine here the proposition that all multiparty quantum states can be made monogamous by considering positive integral powers of any quantum correlation measure. With Rajagopal-Rendell quantum deficit as the measure of quantum correlations for symmetric 3-qubit pure states, we illustrate that monogamy inequality is satisfied for higher powers of quantum deficit. We discuss the drawbacks of this inequality in quantification of correlations in the state. We also prove a monogamy inequality in higher powers of classical mutual information and bring out the fact that such inequality need not necessarily imply restricted shareability of correlations. We thus disprove the utility of higher powers of any correlation measure in establishing monogamous nature in multiparty quantum states.