Existence of maximally correlated states

Abstract

A measure of total correlations cannot increase under deterministic local operations. We show that, for any number of systems, this condition alone does not guarantee the existence of maximally correlated states. Namely, there is no state that simultaneously maximizes all the measures satisfying it. If, in addition, the measures do not increase with probability unity under local measurements, then such states exist for two systems. They are the maximally entangled states. For a larger number of systems, it depends on their Hilbert space dimensions.

Observation of the tradeoff between internal quantum nonseparability and external classical correlations

“…The entanglement (or the quantum nonseparability) between the two subsystems (or degrees of freedom) of A and the total correlations between A and B limit each other [1]. This relation can be described quantitatively using an inequality that involves an entanglement monotone E and a correlation monotone C. Monotone C is required to vanish for product states and to be non-increasing under local operations, i.e., operations that do not affect either A or B [1,18]. Monotone E must vanish for separable states and be non-increasing under local operations and classical communication [2,19].…”