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Physical Review A

Non-Markovian speedup dynamics via quantum cyclic n -switch

Zhen-Dong Wei, Wei Han, Yingjie Zhang, Wei‐Bin Yan, Zhong‐Xiao Man, Yun‐Jie Xia, Qing-Yu Cai

Published Oct 6, 2025• 1 citation
Publisher

Abstract

In this work, we investigate the dynamical process of an open quantum system under the action of quantum cyclic $n$-switch in generalized amplitude-damping channels and depolarizing channels. The quantum cyclic $n$-switch operation is introduced by an external control system. Our results show that the quantum switch can regulate the dynamical behavior of the system dynamics and achieve non-Markovian speedup dynamics. Increasing the dimension of the control system can significantly enhance the evolution speed of the system's non-Markovian dynamics. For the generalized amplitude-damping channels, when the influence of thermal noise is intense, the greater the quantum cyclic $n$-switch is, the lower the initial coherence is, and the more conducive it is to the acceleration of the quantum state evolution speed. In the depolarizing channels, under the action of quantum cyclic $n$-switch, the evolution speed of the system dynamics is directly related to the non-Markovianity and is independent of the initial coherence of the system.

DOI
10.1103/g8y3-xhmq

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In this work, we investigate the dynamical process of an open quantum system under the action of quantum cyclic nnn-switch in generalized amplitude-damping channels and depolarizing channels. The quantum cyclic nnn-switch operation is introduced by an external control system. Our results show that the quantum switch can regulate the dynamical behavior of the system dynamics and achieve non-Markovian speedup dynamics. Increasing the dimension of the control system can significantly enhance the evolution speed of the system's non-Markovian dynamics. For the generalized amplitude-damping channels, when the influence of thermal noise is intense, the greater the quantum cyclic nnn-switch is, the lower the initial coherence is, and the more conducive it is to the acceleration of the quantum state evolution speed. In the depolarizing channels, under the action of quantum cyclic nnn-switch, the evolution speed of the system dynamics is directly related to the non-Markovianity and is independent of the initial coherence of the system.
As is well known, the quantum evolution speed of quantum state can never be accelerated in the Markovian regime without any operators on the system. The Hamiltonian corrections induced by the action of coherent driving forces are often used to fight dissipative and decoherence mechanisms in experiments. For this reason, considering three noisy channels (the phase-flip channel, the amplitude damping channel and the depolarizing channel), we propose a scheme of speedup evolution of an open system by controlling an external unitary coherent driving operator on the system. It is shown that, in the presence of the coherent driving, no-speedup evolution can be transformed into quantum speedup evolution in the Markovian dynamics process. Additionally, under the fixed coherent driving strength in the above three noisy channels, the best way to achieve the most degree of quantum speedup for the system has been acquired by rotating the system with appropriate driving direction angles, respectively. Finally, we conclude that the reason for this acceleration is not the non-Markovian dynamical behavior of the system but due to the oscillation of geometric distance between the initial state and the target final state.
The maximal evolution speed of a quantum system can be represented by quantum speed limit time (QSLT). We investigate the QSLT of a two-qubit system passing through a correlated channel (amplitude damping, phase damping, and depolarizing). By adjusting the correlation parameter of the channel and the initial entanglement, a method to accelerate the evolution speed of the system for some specific channels is proposed. It is shown that, in the amplitude damping channel and the depolarizing channel, QSLT may be shortened in some cases by increasing the correlation parameter of the channel and the initial entanglement, which are in sharp contrast to the phase damping channel. In particular, under depolarizing channels, the transition from no-speedup evolution to speedup evolution for the system can be realized by changing the correlation strength of the channel.
We investigate the dynamical aspects of the quantum switch and find a particular form of quantum memory emerging out of the switch action. We first analyze the loss of information in a general quantum evolution subjected to a quantum switch and propose a measure to quantify the switch-induced memory. We then derive an uncertainty relation between information loss and switch-induced memory. We explicitly consider the example of depolarizing dynamics and show how it is affected by the action of a quantum switch. For a more detailed analysis, we consider both the control qubit and the final measurement on the control qubit as noisy and investigate the said uncertainty relation. Further, while deriving the Lindblad-type dynamics for the reduced operation of the switch action, we identify that the switch-induced memory actually leads to the emergence of non-Markovianity. Interestingly, we demonstrate that the emergent non-Markovianity can be explicitly attributed to the switch operation by comparing it with other standard measures of non-Markovianity. Our investigation thus paves the way forward to understanding the quantum switch as an emerging non-Markovian quantum memory.
Abstract Quantum theory sets a fundamental bound for the minimal time evolution between initial and final state of a system . This bound is called quantum speed limit time , which is used to quantify the speed of evolution of a quantum system. If quantum speed limit time decreases, the evolution keeps on increasing. In this paper, we study the effect of quantum speed limit time in terms of correlated and uncorrelated noise channels like amplitude damping and phase damping channel. We use maximally entangled mixed state as our initial state. We observe the behavior of quantum speed limit time under Markovian and non-Markovian dynamics. We prove that for the special class of our inital state and for the dynamical evolution of a system, there exist a link between quantum speed limit time and non-Markovianity. However, an interesting results were also observed regarding the tightness of bound in Markovian region. Our results shed light on the information back-flow between system and environment in terms of quantum evolution which is useful as a resource in quantum information processing task.
Quantum speed limit (QSL) time under noise has drawn considerable attention in real quantum computational processes. Though non-Markovian noise is found to be able to accelerate quantum evolution for a damped Jaynes—Cummings model, in this work we show that non-Markovianity will slow down the quantum evolution of an experimentally controllable photon system. As an application, QSL time of a photon can be controlled by regulating the relevant environment parameter properly, which nearly reaches the currently available photonic experimental technology.
Gravitational redshift can cause the distortion of photon wave packets; thus, the non-Markovian speedup evolution of a photon system must be controlled by considering gravitational redshift. We analyze the non-Markovian speedup dynamics of a photon system in the amplitude-damping channel or pure-dephasing channel under the effect of gravitational redshift, which is modelled as a beam-splitter operation. We show that the gravitational redshift weakens the non-Markovian dynamical behavior in both channels. For the amplitude-damping channel, the gravitational redshift promotes further speedup evolution of a photon system when the initial coherence of the system is nonzero. A stronger gravitational redshift and larger initial coherence make improving the evolution speed of the photon system easier. For the pure-dephasing channel, the non-Markovian dynamical behavior decreases owing to the gravitational redshift; however, the evolution speed of the photon is not influenced by the gravitational redshift.