Please use this identifier to cite or link to this item: https://doi.org/10.1103/PhysRevA.80.052313
Title: Optimal Lewenstein-Sanpera decomposition of two-qubit states using semidefinite programming
Authors: Thiang, G.C. 
Raynal, P. 
Englert, B.-G. 
Issue Date: 11-Nov-2009
Citation: Thiang, G.C., Raynal, P., Englert, B.-G. (2009-11-11). Optimal Lewenstein-Sanpera decomposition of two-qubit states using semidefinite programming. Physical Review A - Atomic, Molecular, and Optical Physics 80 (5) : -. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevA.80.052313
Abstract: 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 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 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. © 2009 The American Physical Society.
Source Title: Physical Review A - Atomic, Molecular, and Optical Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/115850
ISSN: 10502947
DOI: 10.1103/PhysRevA.80.052313
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