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ENTANGLEMENT OF FORMATION FOR WERNER STATES AND ISOTROPIC STATES VIA LOGICAL GATES

Cesarino Bertini, María Luisa Dalla Chiara, Roberto Leporini

Published Jul 24, 2016• 0 citations
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Abstract

To what extent is a logical characterization of entanglement possible? We investigate some correlations that hold between the concept of entanglement of formation for Werner states and for isotropic states and the probabilistic behavior of some quantum logical gates.
DOI
10.1142/9789813146280_0013

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Werner states are paradigmatic examples of quantum states and play an innovative role in quantum information theory. In investigating the correlating capability of Werner states, we find the curious phenomenon that quantum correlations, as quantified by the entanglement of formation, may exceed the total correlations, as measured by the quantum mutual information. Consequently, though the entanglement of formation is so widely used in quantifying entanglement, it cannot be interpreted as a consistent measure of quantum correlations per se if we accept the folklore that total correlations are measured (or rather upper bounded) by the quantum mutual information.
The entanglement of formation for a class of high-dimensional quantum mixed states is investigated. A special kind of D-computable states is defined and the lower bound of entanglement of formation for a large class of density matrices whose decompositions lie in these D-computable quantum states is obtained. Moreover we present a kind of construction for this special state which is defined by a class of special matrices with two non-zero different eigenvalues and the other eigenvalues are zero. Making use of the D-computable we construct a class of bound entangled states.
We present a new method of constructing sets of states with known entanglement of formation. The method realizes the optimal decomposition families of states. We also derive the additivity of the entanglement of formation and thus calculate the entanglement cost. These results are used to find out the undistillable entanglement of some states. We illustrate our method by investigating the two-qubit state, the separable state, the maximally correlated state, the isotropic state and the Werner state. We also discuss the realization of Werner state in experiment.