Jensen Shannon divergence as a measure of the degree of entanglement

The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJSD) between quantum states. Here we study this distance as a geometrical measure of entanglement and apply it to different families of states.Comment: 5 pages, 2 figures, to appear in the special issue of IJQI "Noise, Information and Complexity at Quantum Scale", eds. S. Mancini and F. Marcheson

Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system

We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei" and Ne "electrons". We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses. Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass. We show how this entanglement feature can be inferred by means of the Born-Oppenheimer Ansatz, whose validity and breakdown can be understood from a quantum information point of view.Comment: Accepted in Eur. Phys. J. D (2014

Typical Behavior of the Global Entanglement of an Open Multiqubit System in a Non-Markovian Regimen

We investigate the decay of the global entanglement, due to decoherence, of multiqubit systems interacting with a reservoir in a non-Markovian regime. We assume that during the decoherence process each qubit of the system interacts with its own, independent environment. Most previous works on this problem focused on particular initial states or families of initial states amenable of analytical treatment. Here we determine numerically the typical, average behavior of the system corresponding to random initial pure states uniformly distributed (in the whole Hilbert space of n-qubit pure states) according to the Haar measure. We study systems consisting of 3, 4, 5, and 6 qubits. In each case we consider also the entanglement dynamics corresponding to important particular initial states, such as the GHZ states or multiqubit states maximizing the global entanglement, and determine in which cases any of these states is representative of the average behavior associated with general initial states.Fil: Majtey, A. P.. Universidad de Granada; EspañaFil: Plastino, Ángel Ricardo. Universidad Nacional de La Plata; Argentina. Universidad de Granada; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentin

Robustness of Highly Entangled Multi-Qubit States Under Decoherence

We investigate the decay of entanglement, due to decoherence, of multi-qubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own, independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness optimization problem, only involving states equivalent under local unitary transformations to the |GHZ> state.Comment: 16 pages, 3 figures. Changes in Sec.

New features of quantum discord uncovered by q-entropies

The notion of quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett 88 (2001) 017901] (see also Henderson and Vedral [J. Phys. A 34 (2001) 6899]) has attracted increasing attention, in recent years, as an entropic quantifier of non-classical features pertaining to the correlations exhibited by bipartite quantum systems. Here we generalize the notion so as to encompass power-law q-entropies (that reduce to the standard Shannon entropy in the limit q→1) and study the concomitant consequences. The ensuing, new discord-like measures we advance describe aspects of non-classicality that are different from those associated with the standard quantum discord. A particular manifestation of this difference concerns a feature related to order. Let D1 stand for the standard, Shannon-based discord measure and Dq for the q≠1 one. If two quantum states A,B are such that D1(A)>D 1(B), this order-relation does not remain invariant under a change from D1 to Dq.Fil: Majtey, A. P.. Universidad de Granada; EspañaFil: Plastino, Ángel Ricardo. Universidad Nacional de La Plata. Centro Regional de Estudios Genómicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Plastino, Ángel Luis. 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