Negativity as a counter of entangled dimensions

TL;DR

This paper demonstrates that negativity, a popular entanglement measure, can be interpreted as an estimator of the number of entangled degrees of freedom in bipartite quantum systems, aiding in quantifying and certifying quantum correlations.

Contribution

It introduces a novel physical interpretation of negativity as a count of entangled degrees of freedom, enabling device-independent bounds and certification of quantum dimensionality.

Findings

Negativity estimates the number of entangled degrees of freedom.

Lower bounds on negativity can be obtained device-independently.

Negativity can certify the quantumness and minimal entangled dimensions.

Abstract

Among all entanglement measures negativity arguably is the best known and most popular tool to quantify bipartite quantum correlations. It is easily computed for arbitrary states of a composite system and can therefore be applied to discuss entanglement in an ample variety of situations. However, its direct physical meaning has not been pointed out yet. We show that the negativity can be viewed as an estimator of how many degrees of freedom of two subsystems are entangled. As it is possible to give lower bounds for the negativity even in a device-independent setting, it is the appropriate quantity to certify quantumness of both parties in a bipartite system and to determine the minimum number of dimensions that contribute to the quantum correlations.