Some Features of the Conditional qq-Entropies of Composite Quantum Systems

The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$ through the quantity $\omega_q = Tr\rho^q$, and admit as a particular instance the standard von Neumann entropy in the limit case $q\to 1$. A comprehensive numerical survey of the space of pure and mixed states of bipartite systems is here performed, in order to determine the volumes in state space occupied by those states exhibiting various special properties related to the signs of their conditional $q$-entropies and to their connections with other separability-related features, including the majorization condition. Different values of the entropic parameter $q$ are considered, as well as different values of the dimensions $N_1$ and $N_2$ of the Hilbert spaces associated with the constituting subsystems. Special emphasis is paid to the analysis of the monotonicity properties, both as a function of $q$ and as a function of $N_1$ and $N_2$, of the various entropic functionals considered.Comment: Submitted for publicatio

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

Entanglement and the Lower Bounds on the Speed of Quantum Evolution

The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state $\psi_I$ may need so as to evolve into a state orthogonal to itself. Recently [V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A {\bf 67}, 052109 (2003)] this bound has been generalized to the case where $\psi_I$ does not necessarily evolve into an orthogonal state, but into any other $\psi_F$. It was pointed out that, for certain classes of states, quantum entanglement enhances the evolution "speed" of composite quantum systems. In this work we provide an exhaustive and systematic QSL study for pure and mixed states belonging to the whole 15-dimensional space of two qubits, with $\psi_F$ a not necessarily orthogonal state to $\psi_I$. We display convincing evidence for a clear correlation between concurrence, on the one hand, and the speed of quantum evolution determined by the action of a rather general local Hamiltonian, on the other one.Comment: 19 pages, 5 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

Separability Criteria and Entanglement Measures for Pure States of N Identical Fermions

The study of the entanglement properties of systems of N fermions has attracted considerable interest during the last few years. Various separability criteria for pure states of N identical fermions have been recently discussed but, excepting the case of two-fermions systems, these criteria are difficult to implement and of limited value from the practical point of view. Here we advance simple necessary and sufficient separability criteria for pure states of N identical fermions. We found that to be identified as separable a state has to comply with one single identity involving either the purity or the von Neumann entropy of the single-particle reduced density matrix. These criteria, based on the verification of only one identity, are drastically simpler than the criteria discussed in the recent literature. We also derive two inequalities verified respectively by the purity and the entropy of the single particle, reduced density matrix, that lead to natural entanglement measures for N-fermion pure states. Our present considerations are related to some classical results from the Hartree-Fock theory, which are here discussed from a different point of view in order to clarify some important points concerning the separability of fermionic pure states.Comment: 6 pages, 0 figure