Comparison of Entropies in the Light of Separability

We introduce an entropy of the form −Tr(ρnlogρ) to investigate quantum mechanical properties, like entanglement, for mixed states. We compare it to other quantum entropies where the power of the density matrix has been used to obtain more information than the Von Neumann entropy. We discuss both the pure state case and the mixed state case (Werner state) with special regard to separability. The power-log entropy is a non-additive entropy and we derive a pseudo additivity condition. The conditional entropy thus defined can be negative for entangled states unlike the classical entropy. The zero leads to the separability criterion. Our results show that for Werner states (with x component of the pure state), a rapid convergence to x = 1/3 as n increases, thus restoring the Pere’s criterion. There are other aspects where power-log entropy is useful. The power of the density matrix defines a map on the state space with pure states as fixed points. The mixed states map to pure states for increasing n.