Feedback control of quantum entanglement in a two-spin system

A pair of spins is the most simple quantum system that can exhibit entanglement: a nonclassical property that plays an essential role in quantum information technologies. In this paper, feedback control problems of a symmetric two-spin system conditioned on a continuous measurement are investigated. In order to make some useful formulas in stochastic control theory directly applicable, we first derive a two-dimensional representation of the system. We then prove that a feedback controller stabilizes an entangled state of the two spins almost globally with probability one. Furthermore, it is demonstrated that some entangled states, which correspond to nonequilibrium points of the dynamics, are globally stabilized via feedback in the sense that the mean distance from a target can be reduced to an arbitrarily small value.