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arXiv:1802.08990 · Scientific Reports

Role of flow of information in the speedup of quantum evolution

J. Wang, Yilun Wu, Ziyang Xie

Published Nov 9, 2018• 10 citations
arXivHTMLPDF

Abstract

Quantum evolution can be accelerated in a non-Markovian environment. Previous results show that the formation of a system-environment bound state governs the quantum speedup. Although a stronger bound state in the system-environment spectrum may seem like it should cause greater speed of evolution, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a classical-driven qubit interacting with a photonic crystal waveguide in the presence of a mirror, resulting in non-Markovian dynamics for the system. Within the considered model, we show the influence of the mirror and the classical field on the evolution speed of the system. In particular, we find that the formation of a bound state is not the essential reason for the acceleration of evolution. The quantum speedup is attributed to the flow of information, regardless of the direction in which the information flows. Our conclusion can also be used in other non-Markovian environments.

DOI
10.1038/s41598-018-34890-x

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Quantum evolution can be accelerated in a non-Markovian environment. Previous results show that the formation of a system-environment bound state governs the quantum speedup. Although a stronger bound state in the system-environment spectrum may seem like it should cause greater speed of evolution, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a classical-driven qubit interacting with a photonic crystal waveguide in the presence of a mirror, resulting in non-Markovian dynamics for the system. Within the considered model, we show the influence of the mirror and the classical field on the evolution speed of the system. In particular, we find that the formation of a bound state is not the essential reason for the acceleration of evolution. The quantum speedup is attributed to the flow of information, regardless of the direction in which the information flows. Our conclusion can also be used in other non-Markovian environments.
Quantum speedup of an open quantum system can be induced by the non-Markovian effect of the environment. Although an environment with a higher degree of non-Markovianity may seem like it should cause a faster speed of quantum evolution, this seemingly intuitive thinking may not always be correct. To clarify this point, we give a mechanism for controlling speedup of a single qubit that is coupled to a hierarchical photonic-crystal (PC) environment, which contains a defect single-mode cavity and a semi-infinite one-dimensional (1D) waveguide. Via studying the dynamics of the qubit, we reveal that with a judicious choice of the qubit-cavity coupling strength and the memory time of the waveguide environment, a speed-up evolution can be achieved. In particular, we found that the quantum speedup is not entirely attributed to the non-Markovianity, but to the increase of the total amount of flow information. That is the intrinsic physical reason that the hierarchical environment may induce the speed-up process. Our results may open new perspectives for detecting quantum speedup in realistic environments.
In this paper, we investigate the relationship between the quantum speedup, non-Markovianity and formation of a system-environment bound state. Previous results show a monotonic relation between these three such that providing bound states with more negative energy can lead to a higher degree of non-Markovianity, and hence to a greater speed of quantum evolution. By studying dynamics of a dissipative two-level system or a V-type three-level system, when similar and additional systems are present, we reveal that the quantum speedup is exclusively related to the formation of the system-environment bound state, while the non-Markovian effect of the system dynamics is neither necessary nor sufficient to speed up the quantum evolution. On the other hand, it is shown that only the formation of the system-environment bound state plays a decisive role in the acceleration of the quantum evolution.
The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interest in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.
We theoretically study the dynamical speedup of a quantum system in a nonequilibrium environment. Based on the trace distance, we derive the generalized Margolus-Levitin and Mandelstam-Tamm types of bounds on the quantum speed limit time of a quantum system evolving from an arbitrary initial state. We demonstrate that the mechanism for the speedup of dynamical evolution is closely associated with both the energy of the system and exchange of information between the system and its environment. It is shown that the nonequilibrium feature of the environment can speed up the quantum evolution in both Markovian and non-Markovian dynamics regions. We emphasize that the non-Markovian effect of the system dynamics is neither necessary nor sufficient to speed up the quantum evolution in a nonequilibrium environment.
We propose a method of accelerating the speed of evolution of an open system by an external classical driving field for a qubit in a zero-temperature structured reservoir. It is shown that, with a judicious choice of the driving strength of the applied classical field, a speed-up evolution of an open system can be achieved in both the weak system-environment couplings and the strong system-environment couplings. By considering the relationship between non-Makovianity of environment and the classical field, we can drive the open system from the Markovian to the non-Markovian regime by manipulating the driving strength of the classical field. That is the intrinsic physical reason that the classical field may induce the speed-up process. In addition, the role of this classical field on the variation of quantum evolution speed in the whole decoherence process is discussed.
Abstract In this study, we propose accelerating the qubit evolution using external classical driving fields in open systems. The results show that the quantum speed limit is determined by the driving strength, population of the initial excited state, and quantum coherence of the initial state. In the Markovian regime, the evolution of the open system will be accelerated by increasing the driving strength, while in non-Markovian regime, the evolution of the open system will present acceleration and deceleration periodically. Moreover, in both Markovian and non-Markovian regime, the population of the initial excited state and the initial-state coherence always can make the quantum speed limit bound tighter.