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Laser Physics

Quantum dynamical speedup in classical colored-noise environments

Ang-Cheng Yang, L. H. Wu, W. W. Cheng

Published Sep 1, 2025• 0 citations
Publisher

Abstract

Abstract In this paper, we have investigated the behavior alterations and properties of the quantum speed limit time (QSLT) under different parameters’ modulations, as well as its relation to the non-Markovianity of the system in the presence of random telegraph noise (RTN) and colored noise (CN). We found that when the switching rate of RTN and the power-law exponent of CN are varied, both QSLT and the non-Markovianity of the system change, and a specific negative correlation exists between them. We have also explored the consistency of the above-mentioned conclusions for both pure and mixed initial states. Our findings may be conducive to uncovering the mechanism of non-Markovian regulation of QSLT and providing possible artificial control schemes for this behavior.

DOI
10.1088/1555-6611/adfdb7

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Abstract In this paper, we have investigated the behavior alterations and properties of the quantum speed limit time (QSLT) under different parameters’ modulations, as well as its relation to the non-Markovianity of the system in the presence of random telegraph noise (RTN) and colored noise (CN). We found that when the switching rate of RTN and the power-law exponent of CN are varied, both QSLT and the non-Markovianity of the system change, and a specific negative correlation exists between them. We have also explored the consistency of the above-mentioned conclusions for both pure and mixed initial states. Our findings may be conducive to uncovering the mechanism of non-Markovian regulation of QSLT and providing possible artificial control schemes for this behavior.
Abstract Random telegraph noise (RTN) has been widely used to describe the environmental effects on open quantum systems. In most cases, it is assumed that the environmental noise described by RTN has symmetric properties. However, in some important physical processes, the asymmetric characteristics of environmental noise play a crucial role in the dynamical evolution of the quantum systems. We theoretically study the dephasing dynamics of a two-level quantum system induced by RTN with asymmetric properties. Within the framework of the stochastic Liouville equation, we derive the exact expression of the decoherence function quantifying the coherence evolution of the quantum system. It is shown that, in contrast to the case of the symmetric RTN, the asymmetric RTN can induce a frequency shift and may lead to non-Markovian behavior in the decoherence dynamics of the quantum system. Furthermore, by adjusting the average transition rate, the transition rate difference, and the transition amplitude difference of the environmental noise, the decoherence dynamics of the quantum system can be effectively modulated.
In this paper, we investigate quantum speed limits (QSLs) of a two-level system in the colored environments which are described by stochastic processes. We present QSL can be affected by the correlation time, the partitions of the constituent elements of the two-level system in different colored environments: the Ornstein–Uhlenbeck environment, simple fluctuating bottleneck environment, and the Dichotomic (two-state) environment. The investigations provide us a potential way to manipulate the quantum speed limit time (QSLT) of the quantum system in the colored environments. Our results could provide different insights on quantum control technologies of QSL and decoherent dynamics for the quantum computation.
We address the non-Markovian character of quantum maps describing the interaction of a qubit with a random classical field. In particular, we evaluate trace- and capacity-based non-Markovianity measures for two relevant classes of environments showing non-Gaussian fluctuations, described respectively by random telegraph noise and colored noise with spectra of the the form $1/{f}^{\ensuremath{\alpha}}$. We analyze the dynamics of both the trace distance and the quantum capacity, and show that the behavior of non-Markovianity based on both measures is qualitatively similar. Our results show that environments with a spectrum that contains a relevant low-frequency contribution are generally non-Markovian. We also find that the non-Markovianity of colored environments decreases when the number of fluctuators realizing the environment increases.
We address the interaction of single- and two-qubit systems with an external transverse fluctuating field and analyze in detail the dynamical decoherence induced by Gaussian noise and random telegraph noise (RTN). Upon exploiting the exact RTN solution of the time-dependent von Neumann equation, we analyze in detail the behavior of quantum correlations and prove the non-Markovianity of the dynamical map in the full parameter range, i.e., for either fast or slow noise. The dynamics induced by Gaussian noise is studied numerically and compared to the RTN solution, showing the existence of (state dependent) regions of the parameter space where the two noises lead to very similar dynamics. We show that the effects of RTN noise and of Gaussian noise are different, i.e., the spectrum alone is not enough to summarize the noise effects, but the dynamics under the effect of one kind of noise may be simulated with high fidelity by the other one.
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.
In this paper, we investigate the connection between quantum speed limit time and non-Markovianity by combining the concept of two-qubit maximally entangled mixed state for various correlated noise channels. In particular, we find an inverse relation between them, which means that the non-Markovian feature of the quantum process leads to speedup of evolution in terms of correlations between successive uses of noise channels because of various. Parameters, such as correlations, entanglement, get involved in it. As a result of this study, new insights are gained into the control of QSL time for open systems, which opens the door to further experimental development toward the development of quantum thermodynamic devices and quantum computers. Our results shed light into trace back of information from environment which might be useful for quantum information processing task.