Gerardo Adesso, The University of Nottingham
Abstract
The correlations of multipartite quantum states can have nonclassical features other than entanglement. After giving a brief overview of the subject, we focus on the issue of establishing a hierarchy between measures of entanglement and compatible measures of general quantum correlations. We analyze a family of measures of general quantum correlations for composite systems, defined in terms of the bipartite entanglement necessarily created between systems and apparatuses during local measurements. For every entanglement monotone $E$, this operational correspondence provides a different measure $Q_E$ of quantum correlations. Examples of such measures are the relative entropy of quantumness, the quantum deficit, and the negativity of quantumness. In general, we prove that any so defined quantum correlation measure is always greater than (or equal to) the corresponding entanglement between the subsystems, $Q_E \ge E$, for arbitrary states of composite quantum systems. In this respect, quantum correlations truly go beyond entanglement. We then discuss the extent up to which they can exist without entanglement, namely whether there are upper bounds on some measure of quantum correlations for separable states of a given dimension. Addressing this largely open question can be very relevant for those applications for which general quantum correlations, and not entanglement, provide the essential resources.