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Locally Accessible Information of Multisite Quantum Ensembles Violates Monogamy

Locally accessible information is a useful information-theoretic physical quantity of an ensemble of multiparty quantum states. We find it has properties akin to quantum as well as classical correlations of single multiparty quantum states. It satisfies monotonicity under local quantum operations and classical communication. However we show that it does not follow monogamy, an important property usually satisfied by quantum correlations, and actually violates any such relation to the maximal extent. Violation is obtained even for locally indistinguishable, but globally orthogonal, multisite ensembles. The results assert that while single multiparty quantum states are monogamous with respect to their shared quantum correlations, ensembles of multiparty quantum states may not be so. The results have potential implications for quantum communication systems.