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Automatica

Feedback control of quantum entanglement in a two-spin system

Naoki Yamamoto, Koji Tsumura, Shinji Hara

Published Apr 17, 2007• 88 citations
Publisher
DOI
10.1016/j.automatica.2006.12.008

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A pair of spins is the most simple quantum system that can possess entanglement, a non-classical property playing an essential role in quantum information technologies. In this paper, feedback control problems of the two-spin system conditioned on a continuous measurement are considered. In order to make some useful formulas in stochastic control theory directly applicable, we first derive a two-dimensional description 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 shown that another entangled state, which corresponds to a non-equilibrium point of the dynamics, is stabilized via feedback in the sense that the expectation of the distance from the target can be made arbitrarily small.
We study the quantum-jump-based feedback control on the entanglement shared between two qubits with one of them subject to decoherence while the other qubit is under the control. This situation is very relevant to a quantum system consisting of nuclear and electron spins in solid states. The possibility of prolonging the coherence time of the dissipative qubit is also explored. Numerical simulations show that the quantum-jump-based feedback control can improve the entanglement between the qubits and prolong the coherence time for the qubit subject directly to decoherence.
A scheme of quantum feedback control in which entanglement swapping is used to construct quantum feedback controller is proposed. The output state of the system to be controlled is entangled with the quantum state of a particle near the actuator through entanglement swapping, which constructs a quantum feedback channel, and two pairs of entangled states, two entanglement swapping processes and a unitary transformer together constitute a quantum controller. This feedback strategy can perform some tasks, such as remote control of entangled states and distant feedback of quantum states, which are not possible using quantum control with classical feedback.