Entropy

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20 pages, 1025 KiB

Open AccessEditor’s ChoiceArticle

Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

by Regina Finsterhölzl, Manuel Katzer, Andreas Knorr and Alexander Carmele

Entropy 2020, 22(9), 984; https://doi.org/10.3390/e22090984 - 4 Sep 2020

Cited by 11 | Viewed by 5922

Abstract

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are [...] Read more.

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of

N = 30

. Full article

(This article belongs to the Special Issue Open Quantum Systems (OQS) for Quantum Technologies)

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10 pages, 9254 KiB

Open AccessArticle

Effect of Self-Oscillation on Escape Dynamics of Classical and Quantum Open Systems

by Minggen Li and Jingdong Bao

Entropy 2020, 22(8), 839; https://doi.org/10.3390/e22080839 - 30 Jul 2020

Cited by 2 | Viewed by 2687

Abstract

We study the effect of self-oscillation on the escape dynamics of classical and quantum open systems by employing the system-plus-environment-plus-interaction model. For a damped free particle (system) with memory kernel function expressed by Zwanzig (J. Stat. Phys. 9, 215 (1973)), which is originated [...] Read more.

We study the effect of self-oscillation on the escape dynamics of classical and quantum open systems by employing the system-plus-environment-plus-interaction model. For a damped free particle (system) with memory kernel function expressed by Zwanzig (J. Stat. Phys. 9, 215 (1973)), which is originated from a harmonic oscillator bath (environment) of Debye type with cut-off frequency

w_{d}

, ergodicity breakdown is found because the velocity autocorrelation function oscillates in cosine function for asymptotic time. The steady escape rate of such a self-oscillated system from a metastable potential exhibits nonmonotonic dependence on

w_{d}

, which denotes that there is an optimal cut-off frequency makes it maximal. Comparing results in classical and quantum regimes, the steady escape rate of a quantum open system reduces to a classical one with

w_{d}

decreasing gradually, and quantum fluctuation indeed enhances the steady escape rate. The effect of a finite number of uncoupled harmonic oscillators N on the escape dynamics of a classical open system is also discussed. Full article

(This article belongs to the Special Issue Open Quantum Systems (OQS) for Quantum Technologies)

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16 pages, 435 KiB

Open AccessEditor’s ChoiceArticle

Evolution Equations for Quantum Semi-Markov Dynamics

by Nina Megier, Andrea Smirne and Bassano Vacchini

Entropy 2020, 22(7), 796; https://doi.org/10.3390/e22070796 - 21 Jul 2020

Cited by 10 | Viewed by 2954

Abstract

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the [...] Read more.

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the corresponding classical concept, guarantees mathematically well-defined master equations, while accounting for a wide range of phenomena, possibly in the non-Markovian regime. In particular, we analyse the emergence of a dephasing term when moving from one type of master equation to the other, by means of several examples. We also investigate the corresponding Redfield-like approximated dynamics, which are obtained after a coarse graining in time. Relying on general properties of the associated classical random process, we conclude that such an approximation always leads to a Markovian evolution for the considered class of dynamics. Full article

(This article belongs to the Special Issue Open Quantum Systems (OQS) for Quantum Technologies)

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28 pages, 1036 KiB

Open AccessArticle

Energy Dissipation and Decoherence in Solid-State Quantum Devices: Markovian versus non-Markovian Treatments

by Rita Claudia Iotti and Fausto Rossi

Entropy 2020, 22(4), 489; https://doi.org/10.3390/e22040489 - 24 Apr 2020

Cited by 4 | Viewed by 3106

Abstract

The design and optimization of new-generation solid-state quantum hardware absolutely requires reliable dissipation versus decoherence models. Depending on the device operational condition, the latter may range from Markov-type schemes (both phenomenological- and microscopic- like) to quantum-kinetic approaches. The primary goal of this paper [...] Read more.

The design and optimization of new-generation solid-state quantum hardware absolutely requires reliable dissipation versus decoherence models. Depending on the device operational condition, the latter may range from Markov-type schemes (both phenomenological- and microscopic- like) to quantum-kinetic approaches. The primary goal of this paper is to review in a cohesive way virtues versus limitations of the most popular approaches, focussing on a few critical issues recently pointed out (see, e.g., Phys. Rev. B 90, 125140 (2014); Eur. Phys. J. B 90, 250 (2017)) and linking them within a common framework. By means of properly designed simulated experiments of a prototypical quantum-dot nanostructure (described via a two-level electronic system coupled to a phonon bath), we shall show that both conventional (i.e., non-Lindblad) Markov models and density-matrix-based non-Markov approaches (i.e., quantum-kinetic treatments) may lead to significant positivity violations. While for the former case the problem is easily avoidable by choosing genuine Lindblad-type dissipation models, for the latter, a general strategy is still missing. Full article

(This article belongs to the Special Issue Open Quantum Systems (OQS) for Quantum Technologies)

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13 pages, 357 KiB

Open AccessArticle

Quantum Dynamics in a Fluctuating Environment

by Xiangji Cai

Entropy 2019, 21(11), 1040; https://doi.org/10.3390/e21111040 - 25 Oct 2019

Cited by 12 | Viewed by 2816

Abstract

We theoretically investigate the dynamics of a quantum system which is coupled to a fluctuating environment based on the framework of Kubo-Anderson spectral diffusion. By employing the projection operator technique, we derive two types of dynamical equations, namely, time-convolution and time-convolutionless quantum master [...] Read more.

We theoretically investigate the dynamics of a quantum system which is coupled to a fluctuating environment based on the framework of Kubo-Anderson spectral diffusion. By employing the projection operator technique, we derive two types of dynamical equations, namely, time-convolution and time-convolutionless quantum master equations, respectively. We derive the exact quantum master equations of a qubit system with both diagonal splitting and tunneling coupling when the environmental noise is subject to a random telegraph process and a Ornstein-Uhlenbeck process, respectively. For the pure decoherence case with no tunneling coupling, the expressions of the decoherence factor we obtained are consistent with the well-known existing ones. The results are significant to quantum information processing and helpful for further understanding the quantum dynamics of open quantum systems. Full article

(This article belongs to the Special Issue Open Quantum Systems (OQS) for Quantum Technologies)

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11 pages, 329 KiB

Open AccessArticle

State Transfer via On-Line State Estimation and Lyapunov-Based Feedback Control for a N-Qubit System

by Sajede Harraz and Shuang Cong

Entropy 2019, 21(8), 751; https://doi.org/10.3390/e21080751 - 31 Jul 2019

Cited by 9 | Viewed by 2950

Abstract

In this paper, we propose a Lyapunov-based state feedback control for state transfer based on the on-line quantum state estimation (OQSE). The OQSE is designed based on continuous weak measurements and compressed sensing. The controlled system is described by quantum master equation for [...] Read more.

In this paper, we propose a Lyapunov-based state feedback control for state transfer based on the on-line quantum state estimation (OQSE). The OQSE is designed based on continuous weak measurements and compressed sensing. The controlled system is described by quantum master equation for open quantum systems, and the continuous measurement operators are derived according to the dynamic equation of system. The feedback control law is designed based on the Lyapunov stability theorem, and a strict proof of proposed control laws are given. At each sampling time, the state is estimated on-line, which is used to design the control law. The simulation experimental results show the effectiveness of the proposed feedback control strategy. Full article

(This article belongs to the Special Issue Open Quantum Systems (OQS) for Quantum Technologies)

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12 pages, 2002 KiB

Open AccessArticle

Enhanced Superdense Coding over Correlated Amplitude Damping Channel

by Yan-Ling Li, Dong-Mei Wei, Chuan-Jin Zu and Xing Xiao

Entropy 2019, 21(6), 598; https://doi.org/10.3390/e21060598 - 16 Jun 2019

Cited by 5 | Viewed by 2839

Abstract

Quantum channels with correlated effects are realistic scenarios for the study of noisy quantum communication when the channels are consecutively used. In this paper, superdense coding is reexamined under a correlated amplitude damping (CAD) channel. Two techniques named as weak measurement and environment-assisted [...] Read more.

Quantum channels with correlated effects are realistic scenarios for the study of noisy quantum communication when the channels are consecutively used. In this paper, superdense coding is reexamined under a correlated amplitude damping (CAD) channel. Two techniques named as weak measurement and environment-assisted measurement are utilized to enhance the capacity of superdense coding. The results show that both of them enable us to battle against the CAD decoherence and improve the capacity with a certain probability. Remarkably, the scheme of environment-assisted measurement always outperforms the scheme of weak measurement in both improving the capacity and successful probability. These notable superiorities could be attributed to the fact that environment-assisted measurement can extract additional information from the environment and thus it performs much better. Full article

(This article belongs to the Special Issue Open Quantum Systems (OQS) for Quantum Technologies)

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11 pages, 1052 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Quantum Probes for Ohmic Environments at Thermal Equilibrium

by Fahimeh Salari Sehdaran, Matteo Bina, Claudia Benedetti and Matteo G. A. Paris

Entropy 2019, 21(5), 486; https://doi.org/10.3390/e21050486 - 12 May 2019

Cited by 23 | Viewed by 3646

Abstract

It is often the case that the environment of a quantum system may be described as a bath of oscillators with an ohmic density of states. In turn, the precise characterization of these classes of environments is a crucial tool to engineer decoherence [...] Read more.

It is often the case that the environment of a quantum system may be described as a bath of oscillators with an ohmic density of states. In turn, the precise characterization of these classes of environments is a crucial tool to engineer decoherence or to tailor quantum information protocols. Recently, the use of quantum probes in characterizing ohmic environments at zero-temperature has been discussed, showing that a single qubit provides precise estimation of the cutoff frequency. On the other hand, thermal noise often spoil quantum probing schemes, and for this reason we here extend the analysis to a complex system at thermal equilibrium. In particular, we discuss the interplay between thermal fluctuations and time evolution in determining the precision attainable by quantum probes. Our results show that the presence of thermal fluctuations degrades the precision for low values of the cutoff frequency, i.e., values of the order

ω_{c} ≲ T

(in natural units). For larger values of

ω_{c}

, decoherence is mostly due to the structure of environment, rather than thermal fluctuations, such that quantum probing by a single qubit is still an effective estimation procedure. Full article

(This article belongs to the Special Issue Open Quantum Systems (OQS) for Quantum Technologies)

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