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Communications in Theoretical Physics

Quantum State Preparation and Protection by Measurement-Based Feedback Control Against Decoherence

Yan Yan, Jian Zou, Lu Wang, Bao-Ming Xu, Chao-Quan Wang, Bin Shao

Published Feb 1, 2015• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/63/2/06

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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 general quantum system interacting with a bath and derive a master equation in the Lindblad form describing the evolution of the whole quantum system subjected to a measurement-based direct quantum feedback control (MDFC). As an example, we consider a qubit coupled with a dephasing environment under the MDFC. We show that for any given pure target state we can always find the corresponding MDFC scheme, which can effectively drive any initial state into this target state. By using an appropriate MDFC scheme with weak measurement we can stabilize a single qubit initially prepared in one of two nonorthogonal states against dephasing noise. Furthermore, we can effectively protect a kind of known mixed states composed of two nonorthogonal states by using the corresponding MDFC scheme.
Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyze a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two nonorthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a nonprojective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement backaction. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realizes the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes.
Abstract A quantum system will both lose and gain excitation through interaction with the environment in a non-zero temperature environment. In this paper, we investigate how a feedback control scheme utilizing weak measurement stabilizes a quantum state which suffers from an environment with finite temperature. Our study has shown that compared with the conventional ‘do-nothing’ and ‘Helstrom’ schemes, this method is much more useful for suppressing decoherence in a generalized amplitude damping (GAD) noise channel. Additionally, for a quantum state, we give the expression of optimum measurement strength, correction angle and the general analytic expression for the optimum fidelity. Additionally, the maximum value of the fidelity improvement can be achieved by controlling the measurement strength, correction angle and the special initial state of the system. More importantly, we find that this approach can not only be helpful for suppressing decoherence in the GAD channel, but can also play a significant role in the amplitude damping noise channel. This phenomenon reveals that in non-zero temperature noise channels, the feedback control scheme via weak measurement can be better for stabilizing a quantum state.
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.
The protection of quantum states is challenging for nonorthogonal states, especially in the presence of noise. Recent research shows that this difficulty can be overcome by feedback control with weak measurements. However, the state-protection schemes proposed recently work optimally only for special quantum states. In this paper, by applying different weak measurements, we extend the idea of the state-protection scheme to include protecting general states. We calculate numerically the optimal parameters and discuss the performance of the scheme. Comparison between this extended scheme and the earlier scheme is also presented.
We propose a scheme of feed-forward control and its reversal for protecting quantum state against decoherence. Before the noise channel our pre-weak measurement and feed-forward are simply to change the protected state into the state almost immune to the noise channel, and after the channel our reversed operations and post-weak measurements are simply to restore the protected state. Unlike most previous state protection schemes, ours only concerns the noise channel and does not care about the protected state. We show that our scheme can effectively protect unknown states, nonorthogonal states, and entangled states against amplitude damping noise. Our scheme has the merit of protecting quantum states against heavy amplitude damping noise, and can perfectly protect some specific nonorthogonal states in an almost deterministic way, which might find some applications in current quantum communication technology. And it is most important that our scheme is experimentally available with current technology.