As it is well known, every bipartite $2\otimes 2$ density matrix can be obtained from Bell decomposable states via local quantum operations and classical communications (LQCC). Using this fact, the Lewenstein-Sanpera decomposition of an arbitrary bipartite $2\otimes 2$ density matrix has been obtained through LQCC action upon Lewenstein-Sanpera decomposition of Bell decomposable states of $2\otimes 2$ quantum systems, where the product states introduced by Wootters in [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)] form the best separable approximation ensemble for Bell decomposable states. It is shown that in these systems the average concurrence of the Lewenstein-Sanpera decomposition is equal to the concurrence of these states.As it is well known, every bipartite $2\otimes 2$ density matrix can be obtained from Bell decomposable states via local quantum operations and classical communications (LQCC). Using this fact, the Lewenstein-Sanpera decomposition of an arbitrary bipartite $2\otimes 2$ density matrix has been obtained through LQCC action upon Lewenstein-Sanpera decomposition of Bell decomposable states of $2\otimes 2$ quantum systems, where the product states introduced by Wootters in [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)] form the best separable approximation ensemble for Bell decomposable states. It is shown that in these systems the average concurrence of the Lewenstein-Sanpera decomposition is equal to the concurrence of these states.

arXiv:quant-ph/0209045Sep 5, 20020 citations

A remark on the Kochen-Specker Theorem

Andrew Lenard

Springer eBooksJan 1, 19744 citations

Optimal Lewenstein-Sanpera decomposition of two-qubit states using semidefinite programming

Guo Chuan Thiang, Philippe Raynal, Berthold‐Georg Englert

We use the language of semidefinite programming and duality to derive necessary and sufficient conditions for the optimal Lewenstein-Sanpera decomposition (LSD) of two-qubit states. We first provide a simple and natural derivation of the Wellens-Ku\ifmmode \acute{s}\else \'{s}\fi{} equations for full-rank states. Then, we obtain a set of necessary and sufficient conditions for the optimal decomposition of rank-3 states. This closes the gap between the full-rank case, where optimality conditions are given by the Wellens-Ku\ifmmode \acute{s}\else \'{s}\fi{} equations, and the rank-2 case, where the optimal decomposition is analytically known. We also give an analytic expression for the optimal LSD of a special class of rank-3 states. Finally, our formulation ensures efficient numerical procedures to return the optimal LSD for any arbitrary two-qubit state.We use the language of semidefinite programming and duality to derive necessary and sufficient conditions for the optimal Lewenstein-Sanpera decomposition (LSD) of two-qubit states. We first provide a simple and natural derivation of the Wellens-Ku\ifmmode \acute{s}\else \'{s}\fi{} equations for full-rank states. Then, we obtain a set of necessary and sufficient conditions for the optimal decomposition of rank-3 states. This closes the gap between the full-rank case, where optimality conditions are given by the Wellens-Ku\ifmmode \acute{s}\else \'{s}\fi{} equations, and the rank-2 case, where the optimal decomposition is analytically known. We also give an analytic expression for the optimal LSD of a special class of rank-3 states. Finally, our formulation ensures efficient numerical procedures to return the optimal LSD for any arbitrary two-qubit state.

arXiv:0909.4599Physical Review ANov 11, 20095 citations

On a conjecture of C.N. Yang

James S. Bell

Physics LettersSep 1, 19626 citations

Lewenstein-Sanpera decomposition For Bell Decomposable

Seyed Javad Akhtarshenas, M. A. Jafarizadeh

We propose a simple geometrical approach for finding the Lewenstein-Sanpera decomposition of Bell decomposable states of 2 otimes 2 quantum systems. We show that in these systems, the weight of the pure entangled part in the decomposition is equal to the concurrence of the state. It is also shown that the optimized separable part of L-S decomposition minimizes the von Neumann relative entropy. We also obtain the decomposition for a class of mixed states by using some LQCC actions. It is also shown that for these states the average concurrence of L-S decomposition is equal to their concurrence.We propose a simple geometrical approach for finding the Lewenstein-Sanpera decomposition of Bell decomposable states of 2 otimes 2 quantum systems. We show that in these systems, the weight of the pure entangled part in the decomposition is equal to the concurrence of the state. It is also shown that the optimized separable part of L-S decomposition minimizes the von Neumann relative entropy. We also obtain the decomposition for a class of mixed states by using some LQCC actions. It is also shown that for these states the average concurrence of L-S decomposition is equal to their concurrence.

arXiv:quant-ph/0207161Jul 28, 20020 citations

A Remark concerning the Bogoliubov Theory

John M. Blatt

Progress of Theoretical PhysicsMar 1, 19590 citations

Lewenstein-Sanpera Decomposition for

2\otimes 2

Systems

As it is well known, every bipartite

2\otimes 2

density matrix can be obtained from Bell decomposable states via local quantum operations and classical communications (LQCC). Using this fact, the Lewenstein-Sanpera decomposition of an arbitrary bipartite

2\otimes 2

density matrix has been obtained through LQCC action upon Lewenstein-Sanpera decomposition of Bell decomposable states of

2\otimes 2

quantum systems, where the product states introduced by Wootters in [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)] form the best separable approximation ensemble for Bell decomposable states. It is shown that in these systems the average concurrence of the Lewenstein-Sanpera decomposition is equal to the concurrence of these states.