Vol.3 No.3
May 12,
2003
Researches:
A matrix realignment method for recognizing entanglement
(pp193202) K. Chen and L.A. Wu
Motivated by the Kronecker product approximation
technique, we have developed a very simple method to assess the
inseparability of bipartite quantum systems, which is based on a
realigned matrix constructed from the density matrix. For any separable
state, the sum of the singular values of the matrix should be less than
or equal to $1$. This condition provides a very simple, computable
necessary criterion for separability,
and shows powerful ability to identify most bound entangled states
discussed in the literature. As a byproduct of the criterion, we give an
estimate for the degree of entanglement of the quantum state.
Local distinguishability of quantum states and the
distillation of
entanglement (pp203210) P.X. Chen and C.Z. Li
This paper tries to probe the relation between the local
distinguishability of orthogonal quantum states and the distillation of
entanglement. An new interpretation for the distillation of entanglement
and the distinguishability of orthogonal quantum states in terms of
information is given, respectively. By constraining our discussion on a
special protocol we give a necessary and sufficient condition for the
local distinguishability of the orthogonal pure states, and gain the
maximal yield of the distillable entanglement. It is shown that the
information entropy, the locally distinguishability of quantum states
and the distillation of entanglement are closely related.
Entanglement transformations of pure Gaussian
states (pp211223) G. Giedke, J. Eisert, J.I.
Cirac, and M.B. Plenio
We present a theory of entanglement transformations of
Gaussian pure states with local Gaussian operations and classical
communication. This is the experimentally accessible set of operations
that can be realized with optical elements such as beam splitters, phase
shifts and squeezers, together with homodyne measurements. We provide a
simple necessary and sufficient condition for the possibility to
transform a pure bipartite Gaussian state into another one. We contrast
our criterion with what is possible if general local operations are
available.
EinsteinPodolskyRosen
correlation seen from moving observers (pp224228) H. Terashima and M. Ueda
Within the framework of relativistic quantum theory, we
consider the EinsteinPodolskyRosen (EPR) gedankenexperiment in which
measurements of the spin are performed by moving observers. We find that
the perfect anticorrelation in the same direction between the EPR pair
no longer holds in the observers' frame. This does not imply a breakdown
of the nonlocal correlation. We explicitly show that the observers must
measure the spin in appropriately chosen different directions in
order to observe the perfect anticorrelation. This fact should be taken
into account in utilizing the entangled state in quantum communication
by moving observers.
LS decomposition for 2x2 density matrix by using
Wootters's basis (pp229248) S.J. Akhtarshenas and M.A.
Jafarizadeh
An analytical expression for optimal LewensteinSanpera
(LS) decomposition of a generic two qubit density matrix is given. By
evaluating the LS decomposition of Bell decomposable states, the
optimal decomposition for arbitrary full rank state of two qubit system
is obtained via local quantum operations and classical communications (LQCC).
In Bell decomposable case the separable state optimizing LS
decomposition, minimize the von Neumann relative entropy as a measure of
entanglement. The LS decomposition for a generic twoqubit density
matrix is only obtained by using Wootters's basis. It is shown that the
average concurrence of the decomposition is equal to the concurrence of
the state. It is also shown that all the entanglement content of the
state is concentrated in the Wootters's state x_1> associated with the
largest eigenvalue \lambda_1 of the Hermitian matrix \sqrt{\sqrt{rho}\tilde{rho}\sqrt{rho}}
. It is shown that a given density matrix rho with corresponding set of
positive numbers \lambda_i and Wootters's basis can transforms under
SO(4,c) into a generic 2x2 matrix with the same set of positive numbers
but with new Wootters's basis, where the local unitary transformations
correspond to SO(4,r) transformations, hence, \rho can be represented as
coset space SO(4,c)/SO(4,r) together with positive numbers lambda_i.
Necessary conditions for efficient simulation of
Hamiltonians using local unitary operations (pp249257)
H. Chen
We study necessary conditions for the efficient
simulation of both bipartite and multipartite Hamiltonians, which are
based on the algebraicgeometric invariants introduced in [12], but
independent of the eigenvalues of Hamiltonians. Our results indicate
that the problem of efficient simulation of Hamiltonians for arbitrary
bipartite or multipartite quantum systems cannot be described by using
only eigenvalues, unlike that in the twoqubit case.
3Local
Hamiltonian is QMAcomplete (pp258264)
J. Kempe and O. Regev
It has been shown by Kitaev that the 5local Hamiltonian
problem is QMAcomplete. Here we reduce the locality of the problem by
showing that 3local Hamiltonian is already QMAcomplete.
Information
theoretic aspects in ponderomotive systems (pp265279)
S. Giannini, S. Mancini and P. Tombesi
We show the possibility to entangle radiation modes
through a simple reflection on a moving mirror. The model of an optical
cavity having a movable end mirror, and supporting different modes is
employed. The mechanical motion of the mirror mediates information
between the modes leading to an effective modemode interaction. We
characterize the modes' entanglement on the basis of recent separability
criteria. The effect of the thermal noise associate to the mirror's
motion is accounted for. Then, we evaluate the performances of such
ponderomotive entanglement in possible applications like teleportation
and telecloning.
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