Optimal Lewenstein-Sanpera decomposition of two-qubit states using Semidefinite Programming
Abstract
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.
Cite
@article{arxiv.0909.4599,
title = {Optimal Lewenstein-Sanpera decomposition of two-qubit states using Semidefinite Programming},
author = {Guo Chuan Thiang and Philippe Raynal and Berthold-Georg Englert},
journal= {arXiv preprint arXiv:0909.4599},
year = {2010}
}
Comments
7 pages. submitted to PRA