Distinguishing classical correlations from quantum correlations

The aim of this paper is to distinguish classical correlations from quantum ones. First, a new characterization of a classical correlated (CC) state is established. Corresponding results for the left and right classical correlations are also obtained. Second, a sufficient and necessary condition for a convex combination of two CC states to be CC is given. It is proved that the set CC(HA otimes HB) of all CC states on HA⊗HB is a perfect, nowhere dense and compact subset of the metric space D(HA otimes HB) of all states (density operators) on (HA otimes HB). Based on our new characterization of CC states, a quantity Q(ρ) is associated with a state ρ. It is shown that a state ρ is CC if and only if Q(ρ) = 0. In particular, we prove that the Werner state Wλ in a two-qubit system with a single real parameter λ is CC if and only if λ = 0.25. (paper)