205 research outputs found
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
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
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
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
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
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