Correlative Capacity of Composite Quantum States

TL;DR

This paper investigates the limits of correlation in quantum states, introducing new theoretical tools to characterize the maximum and minimum correlations possible in various classes of quantum states, including entangled and separable states.

Contribution

It introduces the concepts of infimum and supremum within majorization theory to analyze the correlation capacity of quantum states, providing new bounds and characterizations.

Findings

Maximum separable correlation is an LOCC monotone.

Least disordered states are characterized for different classes.

The framework applies to multi-qubit pure states and classical correlations.

Abstract

We characterize the optimal correlative capacity of entangled, separable, and classically correlated states. Introducing the notions of the infimum and supremum within majorization theory, we construct the least disordered separable state compatible with a set of marginals. The maximum separable correlation information supportable by the marginals of a multi-qubit pure state is shown to be an LOCC monotone. The least disordered composite of a pair of qubits is found for the above classes, with classically correlated states defined as diagonal in the product of marginal bases.