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Special Issue "Quantum Collision Models"

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

Deadline for manuscript submissions: 31 December 2022 | Viewed by 10493

Special Issue Editor

Prof. Dr. Francesco Ciccarello
E-Mail Website
Guest Editor
1. Dipartimento di Fisica e Chimica—Emilio Segrè, University of Palermo, 90128 Palermo, Italy
2. NEST, Istituto Nanoscienze—CNR, I-56127 Pisa, Italy
Interests: quantum optics; open quantum systems; waveguide QED; quantum correlations without entanglement; quantum information processing implementations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Open quantum systems (OQSs) are topical these days. Most notably, their study is essential within the very broad framework of quantum technologies whose full development is hindered by decoherence.

Being inherently difficult to study, OQS dynamics demand effective descriptions and models. In this respect, an emerging approach is to adopt quantum collision models (CMs), also known as repeated interactions schemes; the reservoir is simply described as a collection of smaller units with which the open system interacts one at a time.

First introduced decades ago for investigating weak measurements and micromaser dynamics and then reconsidered in the 2000s from a quantum information theory perspective, the last few years have seen a fast spread of CMs especially in research areas such as quantum non-Markovian dynamics, non-equilibrium quantum thermodynamics, quantum optics, and even gravitational decoherence.

Currently, the number of problems where a collisional approach finds application is growing. Natural questions include: To what extent are CMs a helpful tool? Can we envisage a CM-based approach for tackling potentially any OQS problem? Are there interesting applications of CMs yet unknown? In this spirit, the present Special Issue (the first fully dedicated to CMs to our knowledge) welcomes research papers where quantum CMs are effectively employed for investigating a physical phenomenon, possibly in new areas or when an advantage emerges over more conventional approaches.

Prof. Dr. Francesco Ciccarello
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Open quantum systems
  • Quantum thermodynamics
  • Quantum information
  • Quantum non-Markovianity
  • Non-equilibrium processes

Published Papers (11 papers)

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Research

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Article
Environment-Assisted Modulation of Heat Flux in a Bio-Inspired System Based on Collision Model
Entropy 2022, 24(8), 1162; https://doi.org/10.3390/e24081162 - 20 Aug 2022
Viewed by 470
Abstract
The high energy transfer efficiency of photosynthetic complexes has been a topic of research across many disciplines. Several attempts have been made in order to explain this energy transfer enhancement in terms of quantum mechanical resources such as energetic and vibration coherence and [...] Read more.
The high energy transfer efficiency of photosynthetic complexes has been a topic of research across many disciplines. Several attempts have been made in order to explain this energy transfer enhancement in terms of quantum mechanical resources such as energetic and vibration coherence and constructive effects of environmental noise. The developments in this line of research have inspired various biomimetic works aiming to use the underlying mechanisms in biological light harvesting complexes for the improvement of synthetic systems. In this article, we explore the effect of an auxiliary hierarchically structured environment interacting with a system on the steady-state heat transport across the system. The cold and hot baths are modeled by a series of identically prepared qubits in their respective thermal states, and we use a collision model to simulate the open quantum dynamics of the system. We investigate the effects of system-environment, inter-environment couplings and coherence of the structured environment on the steady state heat flux and find that such a coupling enhances the energy transfer. Our calculations reveal that there exists a non-monotonic and non-trivial relationship between the steady-state heat flux and the mentioned parameters. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Article
Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations
Entropy 2022, 24(6), 824; https://doi.org/10.3390/e24060824 - 14 Jun 2022
Cited by 1 | Viewed by 702
Abstract
We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative [...] Read more.
We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment are preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Article
Efficiency Fluctuations in a Quantum Battery Charged by a Repeated Interaction Process
Entropy 2022, 24(6), 820; https://doi.org/10.3390/e24060820 - 13 Jun 2022
Cited by 1 | Viewed by 636
Abstract
A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction [...] Read more.
A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction process, and the ergotropy characterizes its charge. The working cycle consists in extracting the ergotropy and charging the battery again. We discuss the fluctuating efficiency of the process, among other fluctuating properties. These fluctuations are dominated by the equilibrium distribution and depend weakly on other process properties. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Article
Measured Composite Collision Models: Quantum Trajectory Purities and Channel Divisibility
Entropy 2022, 24(5), 715; https://doi.org/10.3390/e24050715 - 17 May 2022
Viewed by 605
Abstract
We investigate a composite quantum collision model with measurements on the memory part, which effectively probe the system. The framework allows us to adjust the measurement strength, thereby tuning the dynamical map of the system. For a two-qubit setup with a symmetric and [...] Read more.
We investigate a composite quantum collision model with measurements on the memory part, which effectively probe the system. The framework allows us to adjust the measurement strength, thereby tuning the dynamical map of the system. For a two-qubit setup with a symmetric and informationally complete measurement on the memory, we study the divisibility of the resulting dynamics in dependence of the measurement strength. The measurements give rise to quantum trajectories of the system and we show that the average asymptotic purity depends on the specific form of the measurement. With the help of numerical simulations, we demonstrate that the different performance of the measurements is generic and holds for almost all interaction gates between the system and the memory in the composite collision model. The discrete model is then extended to a time-continuous limit. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Article
Steady-State Thermodynamics of a Cascaded Collision Model
Entropy 2022, 24(5), 644; https://doi.org/10.3390/e24050644 - 03 May 2022
Cited by 2 | Viewed by 672
Abstract
We study the steady-state thermodynamics of a cascaded collision model where two subsystems S1 and S2 collide successively with an environment R in the cascaded fashion. We first formulate general expressions of thermodynamics quantities and identify the nonlocal forms of work [...] Read more.
We study the steady-state thermodynamics of a cascaded collision model where two subsystems S1 and S2 collide successively with an environment R in the cascaded fashion. We first formulate general expressions of thermodynamics quantities and identify the nonlocal forms of work and heat that result from cascaded interactions of the system with the common environment. Focusing on a concrete system of two qubits, we then show that, to be able to unidirectionally influence the thermodynamics of S2, the former interaction of S1R should not be energy conserving. We finally demonstrate that the steady-state coherence generated in the cascaded model is a kind of useful resource in extracting work, quantified by ergotropy, from the system. Our results provide a comprehensive understanding on the thermodynamics of the cascaded model and a possible way to achieve the unidirectional control on the thermodynamics process in the steady-state regime. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Article
Multipartite Correlations in Quantum Collision Models
Entropy 2022, 24(4), 508; https://doi.org/10.3390/e24040508 - 05 Apr 2022
Cited by 1 | Viewed by 718
Abstract
Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, and quantum thermometry. A challenge in [...] Read more.
Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, and quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas. Here we develop a tensor network formalism to address both challenges. We show that the induced correlations in the standard collision model are well captured by a matrix product state (a matrix product density operator) if the colliding particles are in pure (mixed) states. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory-kernel master equation. Analyzing the perturbation series for the memory kernel, we go beyond the recent results concerning the leading role of two-point correlations and consider multipoint correlations (Waldenfelds cumulants) that become relevant in the higher-order stroboscopic limits. These results open an avenue for the further analysis of memory effects in collisional quantum dynamics. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Article
Dissipation-Induced Information Scrambling in a Collision Model
Entropy 2022, 24(3), 345; https://doi.org/10.3390/e24030345 - 27 Feb 2022
Cited by 1 | Viewed by 844
Abstract
In this paper, we present a collision model to stroboscopically simulate the dynamics of information in dissipative systems. In particular, an all-optical scheme is proposed to investigate the information scrambling of bosonic systems with Gaussian environmental states. Varying the states of environments, in [...] Read more.
In this paper, we present a collision model to stroboscopically simulate the dynamics of information in dissipative systems. In particular, an all-optical scheme is proposed to investigate the information scrambling of bosonic systems with Gaussian environmental states. Varying the states of environments, in the presence of dissipation, transient tripartite mutual information of system modes may show negative value, signaling the appearance of information scrambling. We also find that dynamical indivisibility based non-Markovianity plays dual roles in affecting the dynamics of information. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Article
Closed-System Solution of the 1D Atom from Collision Model
Entropy 2022, 24(2), 151; https://doi.org/10.3390/e24020151 - 19 Jan 2022
Cited by 4 | Viewed by 562
Abstract
Obtaining the total wavefunction evolution of interacting quantum systems provides access to important properties, such as entanglement, shedding light on fundamental aspects, e.g., quantum energetics and thermodynamics, and guiding towards possible application in the fields of quantum computation and communication. We consider a [...] Read more.
Obtaining the total wavefunction evolution of interacting quantum systems provides access to important properties, such as entanglement, shedding light on fundamental aspects, e.g., quantum energetics and thermodynamics, and guiding towards possible application in the fields of quantum computation and communication. We consider a two-level atom (qubit) coupled to the continuum of travelling modes of a field confined in a one-dimensional chiral waveguide. Originally, we treated the light-matter ensemble as a closed, isolated system. We solve its dynamics using a collision model where individual temporal modes of the field locally interact with the qubit in a sequential fashion. This approach allows us to obtain the total wavefunction of the qubit-field system, at any time, when the field starts in a coherent or a single-photon state. Our method is general and can be applied to other initial field states. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Article
Stochastic Collisional Quantum Thermometry
Entropy 2021, 23(12), 1634; https://doi.org/10.3390/e23121634 - 06 Dec 2021
Cited by 4 | Viewed by 1257
Abstract
We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows us to significantly extend the parameter range for which an advantage [...] Read more.
We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows us to significantly extend the parameter range for which an advantage over the thermal Fisher information is attained. These results are explicitly demonstrated for dephasing interactions and also hold for partial swap interactions. Furthermore, we show that the optimal measurements can be performed locally, thus implying that genuine quantum correlations do not play a role in achieving this advantage. We explicitly confirm this by examining the correlation properties for the deterministic collisional model. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Article
Battery Charging in Collision Models with Bayesian Risk Strategies
Entropy 2021, 23(12), 1627; https://doi.org/10.3390/e23121627 - 02 Dec 2021
Cited by 6 | Viewed by 890
Abstract
We constructed a collision model where measurements in the system, together with a Bayesian decision rule, are used to classify the incoming ancillas as having either high or low ergotropy (maximum extractable work). The former are allowed to leave, while the latter are [...] Read more.
We constructed a collision model where measurements in the system, together with a Bayesian decision rule, are used to classify the incoming ancillas as having either high or low ergotropy (maximum extractable work). The former are allowed to leave, while the latter are redirected for further processing, aimed at increasing their ergotropy further. The ancillas play the role of a quantum battery, and the collision model, therefore, implements a Maxwell demon. To make the process autonomous and with a well-defined limit cycle, the information collected by the demon is reset after each collision by means of a cold heat bath. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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Review

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Review
Quantum Collision Models: A Beginner Guide
Entropy 2022, 24(9), 1258; https://doi.org/10.3390/e24091258 - 07 Sep 2022
Cited by 1 | Viewed by 623
Abstract
In recent years, quantum collision models, sometimes dubbed repeated interaction models, have gained much attention due to their simplicity and their capacity to convey ideas without resorting to technical complications typical of many approaches and techniques used in the field of open quantum [...] Read more.
In recent years, quantum collision models, sometimes dubbed repeated interaction models, have gained much attention due to their simplicity and their capacity to convey ideas without resorting to technical complications typical of many approaches and techniques used in the field of open quantum systems. In this tutorial, we show how to use these models, highlighting their strengths and some technical subtleties often overlooked in the literature. We do this by deriving the Markovian master equation and comparing the standard collisional derivation with the standard microscopic one. We then use the collision model to derive the master equation of a two-level system interacting with either a bosonic or fermionic bath to give the reader a flavour of the real use of the model. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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