The quantumness of correlations revealed in local measurements exceeds entanglement

TL;DR

This paper introduces measures of quantum correlations based on the entanglement generated during local measurements, showing these correlations always exceed or equal entanglement and persist through measurement chains.

Contribution

It establishes a framework linking quantum correlations to entanglement created in local measurements, revealing their hierarchy and invariance in measurement sequences.

Findings

Quantum correlations are always greater than or equal to entanglement.

Quantum correlations and entanglement do not decrease along measurement chains.

Genuine multipartite entanglement in initial states leads to persistent multipartite entanglement in measurement processes.

Abstract

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. We analyze qualitatively and quantitatively the flow of correlations in iterated measurements, showing that general quantum correlations and entanglement can never decrease along von Neumann chains, and that genuine multipartite entanglement in the initial state of the observed system always gives rise to genuine multipartite entanglement among all subsystems and all measurement apparatuses at any level in the chain. Our results provide a comprehensive framework to understand and quantify general quantum correlations in multipartite states.