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Physica Scripta

Tightening of quantum speed limit bound and tracing back information under non-Markovian dynamics

Natasha Awasthi, Dheeraj Kumar Joshi

Published May 20, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/addafb

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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.
Abstract The time required for a given quantum system to evolve is known as the quantum speed limit (QSL), which can be used to characterize the speed of evolution of a quantum system. We study QSL time for Markovian and non-Markovian dynamics. Investigating the effect of QSL under non-unitary evolution is of fundamental interest. In this work, we derive QSL time for maximally entangled state and apply its results under various noise channels. We discuss measure of QSL, how correlations affect the rate of QSL. Further, we carried an investigation on connection between non-Markovianity and QSL. We show that the non Markovian evolution can speed up quantum evolution, therefore lead to smaller QSL time. We have established the connections between correlated channels, information loss and non-Markovianity. This theory may suggest some further connections to retrieve back information from surrounding and preserves decoherence.
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.
Quantum theory sets a bound on the minimal time it takes for a system to evolve from initial state to target state. This bound is called the quantum speed limit (QSL) time. The quantum speed limit time is used to quantify the maximal speed of the quantum evolution. The quantum evolution will be faster if the quantum speed limit time decreases. In this work, we study the quantum speed limit time for an open quantum system in the presence of disturbance in an environment. We use the model which is provided by Ban [Phys. Rev. A 99, 012116 (2019)]. In this model, two quantum systems [Formula: see text] and [Formula: see text] interact with environment sequentially. At first, quantum system [Formula: see text] interacts with the environment [Formula: see text] as an auxiliary system, then quantum system [Formula: see text] starts its interaction with disturbed environment immediately. In this work, we consider the dephasing coupling with two types of environment that has different spectral density: Ohmic and Lorentzian. We observe that, non-Markovian effects will appear in the dynamics of the second quantum system [Formula: see text] due to the interaction of the first quantum system [Formula: see text] with the environment. Given the fact that the quantum speed limit time reduces due to the non-Markovian feature of quantum evolution, we show that disturbance effects will reduce the quantum speed limit time for the dynamics of the second quantum system [Formula: see text].
Abstract The minimum evolution time between multi-qubit quantum states is estimated for non-Markovian quantum channels. We consider the maximally coherent pure and mixed states as well as multi-qubit X states as initial states and discuss the impact of initial coherence and the behaviour of coherence on their speed of evolution for both dephasing and dissipative processes. The role of the non-zero value of initial coherence under information backflow conditions for the non-unital dissipative process is revealed by the flow of quantum speed limit time ( τ QSL ). The trade-off between mixedness and coherence on the speed limit time reveals the nature of the quantum process the states undergo. The complementarity effect between mixedness and coherence is more prominent in the quantum non-unital dissipation process. The parametric trajectory of speed limit time vividly depicts the difference in the evolution of pure and mixed initial states, and this could be used to distinguish between the unital and non-unital channels studied in this work. Our investigation of quantum speed limit time on multi-qubit entangled X states reveals that τ QSL can be identified as a potential dynamical witness to distinguish multi-qubit states in the course of evolution.
Quantum speed limits impose intrinsic lower bounds on the shortest time scale for quantum system evolution. As an emerging paradigm in quantum resource theory, quantum-state texture has attracted research interest amid the rapid advancement of quantum theory. Herein, we investigate the interplay between quantum speed limits and quantum-state texture via several canonical quantifiers, including trace distance, state rugosity and Jensen-Shannon divergence. To demonstrate our findings, we analyze the minimum evolution time of physical systems subject to dephasing and dissipative dynamics. For the Jensen-Shannon divergence, we further explore nonunitary dynamics described by completely positive and trace-preserving maps, taking the amplitude damping channel as a typical example. In addition, we explore the tightness of these bounds in the considered dynamical models. Our results reveal that quantum speed limits derived from quantum-state texture capture the fundamental constraints on quantum evolutionary speed, with promising applications in quantum computing, quantum control and quantum metrology.
The quantum speed limit for open quantum systems in the non-Markovian regime is analyzed. We provide a lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate, and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by a time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.