QIC Abstracts

 Vol.3 No.3  May 12, 2003
A matrix realignment method for recognizing entanglement (pp193-202)
        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 (pp203-210)
        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 (pp211-223)
        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.

Einstein-Podolsky-Rosen correlation seen from moving observers (pp224-228)
        H. Terashima and M. Ueda 
Within the framework of relativistic quantum theory, we consider the Einstein-Podolsky-Rosen (EPR) gedanken-experiment in which measurements of the spin are performed by moving observers. We find that the perfect anti-correlation in the same direction between the EPR pair no longer holds in the observers' frame. This does not imply a breakdown of the non-local correlation. We explicitly show that the observers must measure the spin in appropriately chosen different directions in order to observe the perfect anti-correlation. This fact should be taken into account in utilizing the entangled state in quantum communication by moving observers.

L-S decomposition for 2x2 density matrix by using Wootters's basis (pp229-248)
        S.J. Akhtarshenas and M.A. Jafarizadeh 
An analytical expression for optimal Lewenstein-Sanpera (L-S) decomposition of a generic two qubit density matrix is given. By evaluating the L-S 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 L-S decomposition, minimize the von Neumann relative entropy as a measure of entanglement. The L-S decomposition for a generic two-qubit 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 (pp249-257)
        H. Chen
We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are based on the algebraic-geometric invariants introduced in [1-2], 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 two-qubit case.

3-Local Hamiltonian is QMA-complete (pp258-264)
        J. Kempe and O. Regev
It has been shown by Kitaev that the 5-local Hamiltonian problem is QMA-complete. Here we reduce the locality of the problem by showing that 3-local Hamiltonian is already QMA-complete.

Information theoretic aspects in ponderomotive systems (pp265-279)
        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 mode-mode 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.

Web-corner update (6) (pp280-280)

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