Entanglement Distribution and Entangling Power of Quantum Gates

Quantum gates, that play a fundamental role in quantum computation and other quantum information processes, are unitary evolution operators $\hat U$ that act on a composite system changing its entanglement. In the present contribution we study some aspects of these entanglement changes. By recourse of a Monte Carlo procedure, we compute the so called "entangling power" for several paradigmatic quantum gates and discuss results concerning the action of the CNOT gate. We pay special attention to the distribution of entanglement among the several parties involved

Maximally correlated multipartite quantum states

We investigate quantum states that posses both maximum entanglement and maximum discord between the pertinent parties. Since entanglement (discord) is defined only for bipartite (two qubit) systems, we shall introduce an appropriate sum over of all bi-partitions as the associated measure. The ensuing definition --not new for entanglement-- is thus extended here to quantum discord. Also, additional dimensions within the parties are considered ({\it qudits}). We also discuss nonlocality (in the form of maximum violation of a Bell inequality) for all multiqubit systems. The emergence of more nonlocal states than local ones, all of them possessing maximum entanglement, will be linked, surprisingly enough, to whether quantum mechanics is defined over the fields of real or complex numbers.Comment: 13 pages, 5 figures, 2 table

The statistics of the entanglement changes generated by the Hadamard-CNOT quantum circuit

We consider the change of entanglement of formation $\Delta E$ produced by the Hadamard-CNOT circuit on a general (pure or mixed) state $\rho$ describing a system of two qubits. We study numerically the probabilities of obtaining different values of $\Delta E$, assuming that the initial state is randomly distributed in the space of all states according to the product measure recently introduced by Zyczkowski {\it et al.} [Phys. Rev. A {\bf 58} (1998) 883].Comment: 12 pages, 2 figure

Correlated multipartite quantum states

We investigate quantum states that possess both maximum entanglement and maximum discord between the pertinent parties. Since entanglement (discord) is defined only for bipartite (two-qubit) systems, we use an appropriate sum over all bipartitions as the associated measure. The ensuing definition - not new for entanglement - is thus extended here to quantum discord. Also, additional dimensions within the parties are considered (qudits). We also discuss quantum correlations that induce Mermin's Bell-inequality violation for all multiqubit systems. One finds some differences when quantum mechanics is defined over the field of real or of complex numbers. © 2013 American Physical Society.Fil: Batle, J.. Universitat de Les Illes Balears; EspañaFil: Casas, M.. Universitat de Les Illes Balears; España. Universitat de Les Illes Balears;Fil: Plastino, Ángel Luis. Universitat de Les Illes Balears; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin