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IEEE Transactions on Automatic Control

Protecting Coherence and Entanglement by Quantum Feedback Controls

Jing Zhang, Re-Bing Wu, Chunwen Li, Tzyh‐Jong Tarn

Published Jan 26, 2010• 89 citations
Publisher

Abstract

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.

DOI
10.1109/tac.2009.2039238

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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.
In this paper, we explore the dynamics and protection of quantum coherence in an open system under non-inertial frames by weak measurement and reversal, and design four strategies to protect the quantum coherence of an initial two-qubit entangled state, when the systems suffer from amplitude damping (AD) channel and one subsystem is under non-inertial frames. In practice, there is no strict inertial frames, decoherence and degradation of the quantum coherence caused by the Unruh effect form acceleration will have a significant interaction, therefore it is important to find some means to protect quantum coherence under non-inertial frames.
A scheme for protecting quantum states from both independent and cooperative decoherence is proposed. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into corresponding coherence-preserving states of qubit pairs. In this scheme, amplitude damping (loss of energy) as well as phase damping (dephasing) is prevented by a strategy called ``free-Hamiltonian elimination.'' We further extend the scheme to include quantum gate operations and show that loss and decoherence during such operations can also be prevented.
In this paper, we investigate the entanglement dynamics of a two-qubit entangled state coupled with its noisy environment, and plan to utilize weak measurement and quantum reversal measurement to study the entanglement dynamics under different decoherence channels in noninertial frames. Through the calculations and analyses, it is shown that the weak measurement can prevent entanglement from coupling to the amplitude damping channel, while the system is under the phase damping and flip channels. This protection protocol cannot prevent entanglement but will accelerate the death of entanglement. In addition, if the system is in the noninertial reference frame, then the effect of weak measurement will be weakened for the amplitude damping channel. Nevertheless, for other decoherence channels, the Unruh effect does not affect the quantum weak measurement, the only exception is that the maximum value of entanglement is reduced to √2/2 of the original value in the inertial frames.
Abstract Entanglement is an essential resource for quantum information processing; however, it is highly susceptible to decoherence induced by environmental interactions. In this work, we investigate the entanglement dynamics of a two-qubit system subjected to Markovian noise and explore the effectiveness of external control fields in preserving quantum correlations. Using the Lindblad master equation, we model the evolution of the system under two decoherence channels, namely, amplitude damping (spontaneous emission) and phase damping (dephasing). We introduce periodic driving and optimal control protocols to mitigate entanglement loss and analyze their impact using concurrence as a quantifier of two-qubit entanglement. Our numerical results reveal certain conditions under which sudden death of entanglement can be delayed or even prevented. Additionally, in the case of the initial state being a mixed state, we identify time regimes where entanglement revival occurs, providing insights into quantum error correction strategies. The results contribute to the broader understanding of quantum coherence preservation and have implications for quantum computing, secure quantum communication, and quantum memory design.
This paper investigates the reconstruction and control of quantum decoherence through a novel approach of inverse back-erasure. Traditional decoherence control strategies primarily focus on mitigating the effects of environmental noise, often employing passive shielding or error correction techniques. This work proposes a proactive method utilizing feedback control to actively reverse the decoherence process, thereby enhancing the coherence of quantum states. The core concept involves precisely measuring the quantum system's interaction with its environment and applying corrective actions to counteract the detrimental effects of decoherence. We explore theoretical frameworks based on Hamiltonian engineering and feedback control theory, formulating a mathematical model for the system and outlining the control strategy. The central equation governing the process is: Δψ(t+Δt) = α(t) Δψ(t) + β(t) (H - η(t) ⋅ H') Δψ(t) where Δψ(t+Δt) is the quantum state at time t+Δt, α(t) is the decoherence factor, β(t) is the control factor, H is the Hamiltonian of the system, H' is the environmental Hamiltonian, and η(t) is the feedback control term. The goal is to manipulate β(t) and η(t) to minimize the effect of decoherence. The effectiveness of this approach is discussed in terms of coherence time extension and entanglement preservation. The research contributes a new paradigm for quantum control, offering potential advancements in quantum computing, quantum communication, and quantum sensing. ---