Quantumness of correlations, quantumness of ensembles and quantum data hiding

TL;DR

This paper investigates the quantumness of correlations in quantum ensembles, relating it to quantum data hiding, and introduces measures that connect to entanglement and disturbance under local measurements.

Contribution

It introduces a general framework for quantifying quantumness of correlations, relates it to entanglement, and demonstrates its importance in quantum data hiding schemes.

Findings

Quantumness measures are entanglement monotones for pure states.

Analytical expression for entanglement of disturbance in pure states.

Ensemble quantumness is crucial for effective quantum data hiding.

Abstract

We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We consider a very general framework, but focus on local complete von Neumann measurements as cause of the disturbance, and, later on, on the trace-distance as quantifier of the disturbance. We discuss connections with entanglement and previously defined notions of quantumness of correlations. We prove that a large class of quantifiers of the quantumness of correlations are entanglement monotones for pure bipartite states. In particular, we define an entanglement of disturbance for pure states, for which we give an analytical expression. Such a measure coincides with negativity and concurrence for the case of two qubits. We compute general bounds on disturbance for both single states and ensembles, and consider several examples, including the uniform Haar ensemble of pure states, and pairs of qubit states. Finally, we show that the notion of ensemble quantumness of correlations is most relevant in quantum data hiding. Indeed, while it is known that entanglement is not necessary for a good quantum data hiding scheme, we prove that ensemble quantumness of correlations is.