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Quantum Information Concepts in Open Quantum Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (30 September 2022) | Viewed by 21129

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Guest Editor
1. Dipartimento di Fisica ‘Aldo Pontremoli’, Università degli Studi di Milano, via Celoria 16, 20133 Milan, Italy
2. Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milan, Italy
Interests: open quantum systems; foundations of quantum mechanics; decoherence

E-Mail Website
Guest Editor
1. Dipartimento di Fisica ‘Aldo Pontremoli’, Università degli Studi di Milano, via Celoria 16, 20133 Milan, Italy
2. Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milan, Italy
Interests: open quantum systems; quantum metrology; foundations of quantum mechanics

E-Mail Website
Guest Editor
1. Dipartimento di Fisica ‘Aldo Pontremoli’, Università degli Studi di Milano, via Celoria 16, 20133 Milan, Italy
2. Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milan, Italy
Interests: open quantum systems; quantum information; quantum thermodynamics

Special Issue Information

It has long been recognized that a key feature in determining the behavior of a quantum system is the interaction with the other surrounding quantum degrees of freedom. This aspect is crucial in foundational studies of quantum mechanics aiming at the description of the quantum measurement process. At the same time, it plays a decisive role in the exploitation of quantum effects, especially in view of the implementation of quantum information schemes, quantum thermodynamic devices, and quantum technology applications. The theory of open quantum systems addresses all these challenges. Recent developments in the field have, however, shifted the activity toward considering and understanding the relevance of correlations, both of classical and quantum nature, in the description of the dynamics and measurement of open quantum systems. Indeed, duly keeping correlations into account both at the initial time and in the course of the evolution is a crucial requirement to pave the way for experimental advancements in the field of open quantum systems.

Prof. Dr. Bassano Vacchini
Dr. Andrea Smirne
Dr. Nina Megier
Guest Editors

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Keywords

  • quantum correlations in OQS
  • information flow in OQS
  • non-Markovianity
  • initial correlations
  • quantum measurement
  • quantum incompatibility
  • entropic inequalities in OQS
  • quantum coherence in OQS

Published Papers (10 papers)

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Research

15 pages, 2656 KiB  
Article
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 2 | Viewed by 1634
Abstract
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 Ts and Tb, 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 (DM) 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 DM 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  
Article
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 7 | Viewed by 1395
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  
Article
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 1551
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  
Article
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 3 | Viewed by 2227
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  
Article
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 1937
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  
Article
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 6 | Viewed by 2571
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  
Article
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 6 | Viewed by 2056
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  
Article
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 1504
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  
Article
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 1804
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  
Article
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 2443
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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