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Modern Physics Letters A

Quantum speed limit for maximally entangled mixed state under non-Markovian Regime

Natasha Awasthi, Manish Manish, Dheeraj Kumar Joshi, Soni Sharma

Published May 8, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217732325500701

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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.
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.
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 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.
Abstract The quantum speed limit (QSL) sets a bound on the minimum time required for a quantum system to evolve between two states. For open quantum systems this quantity depends on the dynamical map describing the time evolution in presence of the environment, on the evolution time τ, and on the initial state of the system. We consider a general single qubit open dynamics and show that there is no simple relationship between memory effects and the tightness of the QSL bound. We prove that only for specific classes of dynamical evolutions and initial states, there exists a link between non-Markovianity and the QSL. Our results shed light on the connection between information back-flow between system and environment and the speed of quantum evolution.
The speed of evolution of a qubit undergoing a nonequilibrium environment with spectral density of general ohmic form is investigated. First we reveal non-Markovianity of the model, and find that the non-Markovianity quantified by information backflow of Breuer et al. [ Phys. Rev. Lett . 103 210401 (2009)] displays a nonmonotonic behavior for different values of the ohmicity parameter s in fixed other parameters and the maximal non-Markovianity can be achieved at a specified value s . We also find that the non-Markovianity displays a nonmonotonic behavior with the change of a phase control parameter. Then we further discuss the relationship between quantum speed limit (QSL) time and non-Markovianity of the open-qubit system for any initial states including pure and mixed states. By investigation, we find that the QSL time of a qubit with any initial states can be expressed by a simple factorization law: the QSL time of a qubit with any qubit-initial states are equal to the product of the coherence of the initial state and the QSL time of maximally coherent states, where the QSL time of the maximally coherent states are jointly determined by the non-Markovianity, decoherence factor and a given driving time. Moreover, we also find that the speed of quantum evolution can be obviously accelerated in the wide range of the ohmicity parameter, i.e., from sub-Ohmic to Ohmic and super-Ohmic cases, which is different from the thermal equilibrium environment case.