title: Negativity as an estimator of entanglement dimension.
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, as opposed to logarithmic negativity, 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.
authors.affiliation: Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.
authors.forename: Christopher
authors.initials: C
authors.lastname: Eltschka
authors.affiliation: Departamento de Química Física, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain.
authors.forename: Jens
authors.initials: J
authors.lastname: Siewert