Entropy

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15 pages, 2656 KiB

Open AccessArticle

Quantum Energy Current Induced Coherence in a Spin Chain under Non-Markovian Environments

by Arapat Ablimit, Run-Hong He, Yang-Yang Xie, Lian-Ao Wu and Zhao-Ming Wang

Entropy 2022, 24(10), 1406; https://doi.org/10.3390/e24101406 - 1 Oct 2022

Cited by 3 | Viewed by 1869

We investigate the time-dependent behaviour of the energy current between a quantum spin chain and its surrounding non-Markovian and finite temperature baths, together with its relationship to the coherence dynamics of the system. To be specific, both the system and the baths are [...] Read more.

We investigate the time-dependent behaviour of the energy current between a quantum spin chain and its surrounding non-Markovian and finite temperature baths, together with its relationship to the coherence dynamics of the system. To be specific, both the system and the baths are assumed to be initially in thermal equilibrium at temperature

T_{s}

and

T_{b}

, respectively. This model plays a fundamental role in study of quantum system evolution towards thermal equilibrium in an open system. The non-Markovian quantum state diffusion (NMQSD) equation approach is used to calculate the dynamics of the spin chain. The effects of non-Markovianity, temperature difference and system-bath interaction strength on the energy current and the corresponding coherence in cold and warm baths are analyzed, respectively. We show that the strong non-Markovianity, weak system-bath interaction and low temperature difference will help to maintain the system coherence and correspond to a weaker energy current. Interestingly, the warm baths destroy the coherence while the cold baths help to build coherence. Furthermore, the effects of the Dzyaloshinskii–Moriya (

D M

) interaction and the external magnetic field on the energy current and coherence are analyzed. Both energy current and coherence will change due to the increase of the system energy induced by the

D M

interaction and magnetic field. Significantly, the minimal coherence corresponds to the critical magnetic field which causes the first order phase transition. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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23 pages, 1358 KiB

Open AccessArticle

Disentanglement Dynamics in Nonequilibrium Environments

by Mingli Chen, Haonan Chen, Tao Han and Xiangji Cai

Entropy 2022, 24(10), 1330; https://doi.org/10.3390/e24101330 - 21 Sep 2022

Cited by 8 | Viewed by 1557

Abstract

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the [...] Read more.

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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17 pages, 443 KiB

Open AccessEditor’s ChoiceArticle

Quantum Non-Markovian Environment-to-System Backflows of Information: Nonoperational vs. Operational Approaches

by Adrián A. Budini

Entropy 2022, 24(5), 649; https://doi.org/10.3390/e24050649 - 5 May 2022

Cited by 9 | Viewed by 1707

Abstract

Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a nonoperational approach, defined by the distinguishability [...] Read more.

Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a nonoperational approach, defined by the distinguishability between two system states characterized by different initial conditions, and an operational approach, which is defined by the correlation between different outcomes associated to successive measurement processes performed over the system of interest. The differences, limitations, and vantages of each approach are characterized in detail by considering diverse system–environment models and dynamics. As a specific example, we study a non-Markovian depolarizing map induced by the interaction of the system of interest with an environment characterized by incoherent and coherent self-dynamics. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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13 pages, 2485 KiB

Open AccessArticle

Effect of Quantum Coherence on Landauer’s Principle

by Kazunari Hashimoto and Chikako Uchiyama

Entropy 2022, 24(4), 548; https://doi.org/10.3390/e24040548 - 13 Apr 2022

Cited by 4 | Viewed by 2446

Abstract

Landauer’s principle provides a fundamental lower bound for energy dissipation occurring with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower bound (entropic bound), recent efforts have also provided another lower [...] Read more.

Landauer’s principle provides a fundamental lower bound for energy dissipation occurring with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower bound (entropic bound), recent efforts have also provided another lower bound associated with the thermal fluctuation of the dissipated energy (thermodynamic bound). The coexistence of the two bounds has stimulated comparative studies of their properties; however, these studies were performed for systems where the time-evolution of diagonal (population) and off-diagonal (coherence) elements of the density matrix are decoupled. In this paper, we aimed to broaden the comparative study to include the influence of quantum coherence induced by the tilted system–reservoir interaction direction. By examining their dependence on the initial state of the information-bearing system, we find that the following properties of the bounds are generically held regardless of whether the influence of the coherence is present or not: the entropic bound serves as the tighter bound for a sufficiently mixed initial state, while the thermodynamic bound is tighter when the purity of the initial state is sufficiently high. The exception is the case where the system dynamics involve only phase relaxation; in this case, the two bounds coincide when the initial coherence is zero; otherwise, the thermodynamic bound serves the tighter bound. We also find the quantum information erasure inevitably accompanies constant energy dissipation caused by the creation of system–reservoir correlation, which may cause an additional source of energetic cost for the erasure. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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23 pages, 1174 KiB

Open AccessArticle

Memory Effects in High-Dimensional Systems Faithfully Identified by Hilbert–Schmidt Speed-Based Witness

by Kobra Mahdavipour, Mahshid Khazaei Shadfar, Hossein Rangani Jahromi, Roberto Morandotti and Rosario Lo Franco

Entropy 2022, 24(3), 395; https://doi.org/10.3390/e24030395 - 12 Mar 2022

Viewed by 2130

Abstract

A witness of non-Markovianity based on the Hilbert–Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful, being easily computable since no diagonalization of the system density matrix [...] Read more.

A witness of non-Markovianity based on the Hilbert–Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful, being easily computable since no diagonalization of the system density matrix is required. We investigate the sensitivity of this HSS-based witness to detect non-Markovianity in various high-dimensional and multipartite open quantum systems with finite Hilbert spaces. We find that the time behaviors of the HSS-based witness are always in agreement with those of quantum negativity or quantum correlation measure. These results show that the HSS-based witness is a faithful identifier of the memory effects appearing in the quantum evolution of a high-dimensional system with a finite Hilbert space. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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13 pages, 459 KiB

Open AccessFeature PaperArticle

Non-Markovian Quantum Dynamics in a Squeezed Reservoir

by Valentin Link, Walter T. Strunz and Kimmo Luoma

Entropy 2022, 24(3), 352; https://doi.org/10.3390/e24030352 - 28 Feb 2022

Cited by 9 | Viewed by 2779

Abstract

We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a [...] Read more.

We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system–environment coupling strength and, thus, the strength of the dissipation. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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15 pages, 9833 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Correlations, Information Backflow, and Objectivity in a Class of Pure Dephasing Models

by Nina Megier, Andrea Smirne, Steve Campbell and Bassano Vacchini

Entropy 2022, 24(2), 304; https://doi.org/10.3390/e24020304 - 21 Feb 2022

Cited by 7 | Viewed by 2293

Abstract

We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of [...] Read more.

We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of freedom that qualitatively and quantitatively affects the correlation profiles, but nevertheless results in the same reduced dynamics for the system. We apply recently developed tools for the characterisation of non-Markovianity to carefully assess the role that correlations, as quantified by the (quantum) Jensen–Shannon divergence and relative entropy, as well as changes in the environmental state, play in whether the conditions for classical objectivity within the quantum Darwinism paradigm are met. We demonstrate that for precisely the same non-Markovian reduced dynamics of the system arising from different microscopic models, some exhibit quantum Darwinistic features, while others show that no meaningful notion of classical objectivity is present. Furthermore, our results highlight that the non-Markovian nature of an environment does not a priori prevent a system from redundantly proliferating relevant information, but rather it is the system’s ability to establish the requisite correlations that is the crucial factor in the manifestation of classical objectivity. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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13 pages, 1199 KiB

Open AccessEditor’s ChoiceArticle

Engineering Classical Capacity of Generalized Pauli Channels with Admissible Memory Kernels

by Katarzyna Siudzińska, Arpan Das and Anindita Bera

Entropy 2021, 23(11), 1382; https://doi.org/10.3390/e23111382 - 21 Oct 2021

Cited by 5 | Viewed by 1625

Abstract

In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian [...] Read more.

In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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12 pages, 602 KiB

Open AccessArticle

Thermodynamics of Reduced State of the Field

by Stefano Cusumano and Łukasz Rudnicki

Entropy 2021, 23(9), 1198; https://doi.org/10.3390/e23091198 - 11 Sep 2021

Cited by 1 | Viewed by 1947

Abstract

Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), [...] Read more.

Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of these solutions. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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8 pages, 1014 KiB

Open AccessEditor’s ChoiceArticle

Quantum Speed Limit and Divisibility of the Dynamical Map

by Jose Teittinen and Sabrina Maniscalco

Entropy 2021, 23(3), 331; https://doi.org/10.3390/e23030331 - 11 Mar 2021

Cited by 10 | Viewed by 2631

Abstract

The quantum speed limit (QSL) is the theoretical lower limit of the time for a quantum system to evolve from a given state to another one. Interestingly, it has been shown that non-Markovianity can be used to speed-up the dynamics and to lower [...] Read more.

The quantum speed limit (QSL) is the theoretical lower limit of the time for a quantum system to evolve from a given state to another one. Interestingly, it has been shown that non-Markovianity can be used to speed-up the dynamics and to lower the QSL time, although this behaviour is not universal. In this paper, we further carry on the investigation on the connection between QSL and non-Markovianity by looking at the effects of P- and CP-divisibility of the dynamical map to the quantum speed limit. We show that the speed-up can also be observed under P- and CP-divisible dynamics, and that the speed-up is not necessarily tied to the transition from P-divisible to non-P-divisible dynamics. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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