Entanglement generation in double-Λ\Lambda system

In this paper, we study the generation of entanglement in a double-$\Lambda$ system. Employing standard method of laser theory, we deduce the dynamic evolution equation of the two-mode field. We analyze the available entanglement criterion for double-$\Lambda$ system and the condition of entanglement existence. Our results show that under proper parameters, the two-mode field can entangled and amlified

Truncated su(2) moment problem for spin and polarization states

We address the problem whether a given set of expectation values is compatible with the first and second moments of the generic spin operators of a system with total spin j. Those operators appear as the Stokes operator in quantum optics, as well as the total angular momentum operators in the atomic ensemble literature. We link this problem to a particular extension problem for bipartite qubit states; this problem is closely related to the symmetric extension problem that has recently drawn much attention in different contexts of the quantum information literature. We are able to provide operational, approximate solutions for every large spin numbers, and in fact the solution becomes exact in the limiting case of infinite spin numbers. Solutions for low spin numbers are formulated in terms of a hyperplane characterization, similar to entanglement witnesses, that can be efficiently solved with semidefinite programming.Comment: 18 pages, 1 figur