Optimal Lewenstein-Sanpera decomposition of two-qubit states using Semidefinite Programming

Details Optimal Lewenstein-Sanpera decomposition of two-qubit states using Semidefinite Programming Optimal Lewenstein-Sanpera decomposition of two-qubit states using Semidefinite Programming

2009-09-25

arxiv.org/abs/0909.4599v1

Phys. Rev. A 80, 052313 (2009)

Physics

Quantum Physics

7 pages. submitted to PRA

Scientific paper

10.1103/PhysRevA.80.052313

We use the language of semidefinite programming and duality to derive necessary and sufficient conditions for the optimal Lewenstein-Sanpera Decomposition (LSD) of 2-qubit states. We first provide a simple and natural derivation of the Wellens-Kus 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-Kus 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 2-qubit state.

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