Feedback control of quantum entanglement in a two-spin system

Authors:
Naoki Yamamoto;Koji Tsumura;Shinji Hara
Affiliations:
Control and Dynamical Systems, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA;Department of Information Physics and Computing, Graduate School of Information Science and Technology, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan;Department of Information Physics and Computing, Graduate School of Information Science and Technology, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Abstract

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.