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Physical Review A

Composite control for protecting two nonorthogonal qubit states against decoherence

Ya Cao, Guojing Tian, Zhichao Zhang, Ying‐Hui Yang, Qiaoyan Wen, Fei Gao

Published Mar 9, 2017• 9 citations
Publisher

Abstract

Quantum feedback control (QFBC) and quantum feedforward control (QFFC) are two of the major techniques for protecting two nonorthogonal qubit states against decoherence. In this paper, we propose a quantum composite control scheme for protecting such states, where QFBC and QFFC are combined. Note that the combination is deliberately devised, other than simply one plus one (i.e., the trivial combination). We show the performance of our scheme is better than that of both the previous control schemes and the trivially combined one for most states and noises in the sense that, for given success probability, our scheme can achieve the biggest fidelity, and for given fidelity, our scheme has the biggest success probability. Furthermore, our scheme can be experimentally implemented with current technologies.

DOI
10.1103/physreva.95.032313

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Quantum feedback control (QFBC) and quantum feedforward control (QFFC) are two of the major techniques for protecting two nonorthogonal qubit states against decoherence. In this paper, we propose a quantum composite control scheme for protecting such states, where QFBC and QFFC are combined. Note that the combination is deliberately devised, other than simply one plus one (i.e., the trivial combination). We show the performance of our scheme is better than that of both the previous control schemes and the trivially combined one for most states and noises in the sense that, for given success probability, our scheme can achieve the biggest fidelity, and for given fidelity, our scheme has the biggest success probability. Furthermore, our scheme can be experimentally implemented with current technologies.
The goal of quantum control is to enable robust quantum information processing in noisy environments. Quantum feedback control is one of the most established strategies, but its reliance on measurement and real-time feedback imposes intrinsic limitations from measurement backaction and latency. Here, we propose and experimentally realize a measurement-free quantum feedforward control scheme, together with a composite framework that sequentially combines quantum feedforward control and quantum feedback control. We demonstrate both theoretically and experimentally that quantum feedforward control effectively protects nonorthogonal quantum states without measurement, while the composite strategy achieves superior performance when measurement is available, which makes it a practical alternative to quantum feedback control. These results establish quantum feedforward control as an independent control approach beyond quantum feedback control and highlight the advantages of the composite scheme, providing a new route toward high-fidelity quantum information processing in noisy environments.
We study protection of a qubit that transfer through a decoherence noise by quantum control technique. In this work, we assume that the communication participants have some side information about the qubit. Our aim is to take fully advantage of given side information to design a quantum control scheme that makes the output state close to the input state as better as possible. Especially, in this paper, we consider the quantum composite control (QCC) structure, which has shown to capture a better balance between fidelity and success probability, i.e., two essential measures for protection. Comparison has been made between our scheme and previous ones. We show there's advantages in two aspects. On one hand, when compared with the scheme that has taking fully consideration of classical side information but not quantum one, our scheme achieves higher fidelity. Inversely, when the scheme with quantum side information but not classical one is considered, our scheme also has nontrivial improvement.
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.
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.
One of the crucial tasks in quantum systems is to reduce the effects of decoherence due to the unavoidable interactions between a system and its environment. Many protection schemes have been proposed recently, among them the weak measurement quantum measurement reversal (WMQMR), weak measurement-based quantum feedback control (QFBC) and quantum feedforward control (QFFC) are reviewed in this paper. By considering weak measurement, the aim is to find a balance between information gain and disturbance of the system caused by the measurement. We classify different types of measurement and give the definition of noise sources and their effects on the state of the system. Finally, we compare and analyze the performance of the discussed protection schemes for different noise sources by numerical simulations.
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.