BEST SEPARABLE APPROXIMATION WITH SEMI-DEFINITE PROGRAMMING METHOD
M. A. Jafarizadeh, Mehdi Mirzaee, M. Rezaee · International Journal of Quantum Information · 2004
The present methods for obtaining the optimal Lewenestein–Sanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein–Sanpera decomposition by using semi-definite programming. In particular, we obtain the optimal Lewenstein–Sanpera decomposition for some examples such as: the Bell decomposable state, the iso-concurrence state, the generic two-qubit state in the Wootters basis, the 2⊗3 Bell decomposable state, the d⊗d Werner and isotropic states, a one parameter 3⊗3 state, and finally a multi-partite isotropic state.