Detection Power of Separability Criteria Based on a Correlation Tensor: A Case Study

Detection power of separability criteria based on a correlation tensor is tested within a family of generalized isotropic states in [Formula: see text]. For [Formula: see text] all these criteria are weaker than the positive partial transposition (PPT) criterion. Interestingly, our analysis supports the recent conjecture that a criterion based on symmetrically informationally complete positive operator-valued measure (SIC-POVMs) is stronger than realignment criterion.

Quantum correlation based on weak measurements

A quantum correlation [Formula: see text] based on weak measurements for bipartite systems is introduced. It is shown that the product states do not contain this quantum correlation. Also, the necessary and sufficient condition for any two-qubit state becoming a product state is obtained. The quantum correlation [Formula: see text] and other quantum correlation for two-qubit entangled pure state, Werner states and isotropic states are compared.

On the Activation of Quantum Nonlocality

<p>We report on some quantum properties of physical systems, namely, entanglement, nonlocality, k-copy nonlocality (superactivation of nonlocality), hidden nonlocality (activation of nonlocality through local filtering) and the activation of nonlocality through tensoring and local filtering. The aim of this work is two-fold. First, we provide a review of the numerical procedures that must be followed in order to calculate the aforementioned properties, in particular, for any two-qubit system, and reproduce the bounds for two-qudit Werner states. Second, we use such numerical tools to calculate new bounds of these properties for two-qudit Isotropic states and two-qubit Hirsch states.</p>

QUANTUM DISCORD DERIVED FROM TSALLIS ENTROPY

Due to some ambiguity in the definition of mutual Tsallis entropy in classical probability theory, its generalization to quantum theory is discussed and, as a consequence, two types of generalized quantum discords, called q-discords, are defined in terms of quantum Tsallis entropy. Both q-discords for two-qubit Werner and isotropic states are determined and compared and it is shown that one of them is non-negative, at least for states under investigation, for all q > 0. Finally, an analytical expression for q-discord of certain family of two-qubit X-states is presented. Using this example, we show that both types of q-discords can take negative values for some q > 1, hence their use as correlations measures is rather limited.