159 research outputs found
Nonlocality and entanglement in qubit systems
Nonlocality and quantum entanglement constitute two special aspects of the
quantum correlations existing in quantum systems, which are of paramount
importance in quantum-information theory. Traditionally, they have been
regarded as identical (equivalent, in fact, for pure two qubit states, that is,
{\it Gisin's Theorem}), yet they constitute different resources. Describing
nonlocality by means of the violation of several Bell inequalities, we obtain
by direct optimization those states of two qubits that maximally violate a Bell
inequality, in terms of their degree of mixture as measured by either their
participation ratio or their maximum eigenvalue
. This optimum value is obtained as well, which coincides with
previous results. Comparison with entanglement is performed too. An example of
an application is given in the XY model. In this novel approximation, we also
concentrate on the nonlocality for linear combinations of pure states of two
qubits, providing a closed form for their maximal nonlocality measure. The case
of Bell diagonal mixed states of two qubits is also extensively studied.
Special attention concerning the connection between nonlocality and
entanglement for mixed states of two qubits is paid to the so called maximally
entangled mixed states. Additional aspects for the case of two qubits are also
described in detail. Since we deal with qubit systems, we will perform an
analogous study for three qubits, employing similar tools. Relation between
distillability and nonlocality is explored quantitatively for the whole space
of states of three qubits. We finally extend our analysis to four qubit
systems, where nonlocality for generalized Greenberger-Horne-Zeilinger states
of arbitrary number of parties is computed.Comment: 16 pages, 3 figure
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 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
Maximally Entangled Mixed States and Conditional Entropies
The maximally entangled mixed states of Munro, James, White, and Kwiat [Phys.
Rev. A {\bf 64} (2001) 030302] are shown to exhibit interesting features vis a
vis conditional entropic measures. The same happens with the Ishizaka and
Hiroshima states [Phys. Rev. A {\bf 62} 022310 (2000)], whose
entanglement-degree can not be increased by acting on them with logic gates.
Special types of entangled states that do not violate classical entropic
inequalities are seen to exist in the space of two qubits. Special meaning can
be assigned to the Munro {\it et al.} special participation ratio of 1.8
The statistics of the entanglement changes generated by the Hadamard-CNOT quantum circuit
We consider the change of entanglement of formation produced by
the Hadamard-CNOT circuit on a general (pure or mixed) state describing
a system of two qubits. We study numerically the probabilities of obtaining
different values of , 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
Some Features of the Conditional -Entropies of Composite Quantum Systems
The study of conditional -entropies in composite quantum systems has
recently been the focus of considerable interest, particularly in connection
with the problem of separability. The -entropies depend on the density
matrix through the quantity , and admit as a
particular instance the standard von Neumann entropy in the limit case . 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 -entropies and to their connections with
other separability-related features, including the majorization condition.
Different values of the entropic parameter are considered, as well as
different values of the dimensions and 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 and as a
function of and , of the various entropic functionals considered.Comment: Submitted for publicatio
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 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 does not necessarily evolve into an
orthogonal state, but into any other . 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 a not necessarily orthogonal
state to . 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
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