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理论物理通讯：英文版

Markov Quantum Feedback Control Based on Homodyne Measurement of a Two-Qubit System

祝敬敏, Shun-Jin Wang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

We consider the system consisting of two qubits collectively damped,with the output being unit-efficiencymeasured and subsequently fed back to control the system state.Our primary goal in this paper is (ⅰ) to solve thefeedback-modified master equation,(ⅱ) to demonstrate the ability of feedback control based on the solutions,and (ⅲ) topick out different steady states by choosing different driving strengths and feedback strengths to counteract the effects ofboth damping and the measurement back-action on the system.We further investigate some properties of the equilibriumsteady state,its distribution probability and entanglement vs.the driving and feedback amplitudes.We find that in ourfeedback model feedback plays a negative role in producing entanglement.

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We consider the system consisting of two qubits collectively damped,with the output being unit-efficiencymeasured and subsequently fed back to control the system state.Our primary goal in this paper is (ⅰ) to solve thefeedback-modified master equation,(ⅱ) to demonstrate the ability of feedback control based on the solutions,and (ⅲ) topick out different steady states by choosing different driving strengths and feedback strengths to counteract the effects ofboth damping and the measurement back-action on the system.We further investigate some properties of the equilibriumsteady state,its distribution probability and entanglement vs.the driving and feedback amplitudes.We find that in ourfeedback model feedback plays a negative role in producing entanglement.
We consider the system consisting of two qubits collectively damped,with the output being unit-efficiency measured and subsequently fed back to control the system state.Our primary goal in this paper is (ⅰ) to solve the feedback-modified master equation,(ⅱ) to demonstrate the ability of feedback control based on the solutions,and (ⅲ) to pick out different steady states by choosing different driving strengths and feedback strengths to counteract the effects of both damping and the measurement back-action on the system.We further investigate some properties of the equilibrium steady state,its distribution probability and entanglement vs.the driving and feedback amplitudes.We find that in our feedback model feedback plays a negative role in producing entanglement.
We consider the system consisting of two qubits collectively damped, with the output being unit-efficiency measured and subsequently fed back to control the system state. Our primary goal in this paper is (i) to solve the feedback-modified master equation, (ii) to demonstrate the ability of feedback control based on the solutions, and (iii) to pick out different steady states by choosing different driving strengths and feedback strengths to counteract the effects of both damping and the measurement back-action on the system. We further investigate some properties of the equilibrium steady state, its distribution probability and entanglement vs. the driving and feedback amplitudes. We find that in our feedback model feedback plays a negative role in producing entanglement.
For two two-level atoms coupled to a single Bosonic mode that is driven and heavily damped, the steady state can be entangled by resonantly driving the system [S. Schneider and G. J. Milburn, Phys. Rev. A 65, 042107 (2002)]. We present a scheme to significantly increase the steady-state entanglement by using homodyne-mediated feedback, in which the Bosonic mode is that of an electromagnetic cavity, the output of which is measured and the resulting homodyne photocurrent is used to modulate the field driving the qubits. Such feedback can increase the nonlinear response to both the decoherence process of the two-qubit system and the coherent evolution of individual qubits. We present the properties of the entangled states using the SO(3) QQQ function.
When a quantum system interacts with its environment, the so-called decoherence effect will normally destroy the coherence in the quantum state and the entanglement between its subsystems. We propose a feedback control strategy based on quantum weak measurements to protect coherence and entanglement of the quantum state against environmental disturbance. For a one-qubit quantum system under amplitude damping and dephasing decoherence channels, our strategy can preserve the coherence based on the measured information about the population difference between its two levels. For a two-qubit quantum system disentangled by independent amplitude damping and dephasing decoherence channels, the designed feedback control can preserve coherence between the ground state and the highest excited states by tuning the coupling strength between the two qubits, and at the same time minimize the loss of entanglement between the two qubits. As a consequence of dynamic symmetry, the generalization of these results derives the concept of control-induced decoherence-free observable subspace, for which several criteria are provided.
We consider an open quantum system subjected to a noise channel under measurement-based feedback control and two prototypical classes of decoherence channels are considered: phase damping and generalized amplitude damping. Based on quantum trajectory theory, we obtain an extended master equation for the dynamics of the reduced system in the presence of feedback control. For a qubit system we analytically solve this master equation and obtain the solution of the state vector dynamics. Then we propose an effective feedback control scheme for preparing an arbitrary quantum pure state. We also study how to protect two nonorthogonal states effectively, and find that projective measurement with unbiased basis is not optimal for this task, while weak measurement with biased basis could realize the best protection of two nonorthogonal states. Furthermore, the inefficiencies in the feedback process are also discussed.
We consider a model consisting of two (two-level) atoms which are placed in two separated heavily damped cavities respectively. We show that the quantum-jump-based feedback based on joint measurement can be used to generate a steady entangled state between two atoms against decoherence. We analyse the effects of general local control Hamiltonians in the performance of entanglement production and show that by choosing a proper control Hamiltonian the steady maximal entanglement between two separated atoms can be protected.