Special Issue "Quantum Entropies and Complexity"

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

Deadline for manuscript submissions: closed (15 September 2019).

Special Issue Editor

Guest Editor
Assoc. Prof. Dr. Fabio Benatti Website E-Mail
Department of Physics, University of Trieste, I-34151 Trieste, Italy
Interests: many-body open quantum systems; quantum correlations in mesoscopic quantum systems; entropy and complexity in quantum dynamics

Special Issue Information

Dear Colleagues,

Revolutionary recent advances in quantum information, communication, and computation have involved the ubiquitous use of entropy-related concepts as fundamental tools to monitor and quantify the complex behavior of quantum systems, by themselves as in quantum dynamics and quantum phase-transitions, and in relation to the manipulation of information they can carry. Quantum entropy, relative entropy, mutual information, and their dynamics are at the core of many disciplines. On the one hand, their purpose is to use quantum mechanics to augment the efficiency of known classical information protocols by using such correlations as quantum entanglement and discord; on the other hand, their aim is to assess how such correlations are created by either physical processes or by suitably engineered ones, especially in many-body quantum systems. One of the goals is to devise quantum protocols that might boost revolutionary practical applications in fields as varied as quantum machine learning, quantum transport processes, quantum metrology, and quantum thermodynamics. In all these different scenarios, entropy-related concepts stand out as fundamental tools with which to capture the complexity of the processes involved and to harness them to the advantage of increasing the efficiency of protocols, by establishing and reaching their ultimate quantum limits.

Prof. Fabio Benatti
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 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

  • quantum information sources and complexity
  • quantum capacities
  • quantum entanglement
  • quantum channels and communications
  • quantum open systems and transport
  • quantum phase-transitions
  • quantum thermodynamics
  • quantum metrology and entanglement
  • quantum neural networks
  • quantum machine learning

Published Papers (3 papers)

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Research

Open AccessFeature PaperArticle
Quantum Thermodynamics in the Refined Weak Coupling Limit
Entropy 2019, 21(8), 725; https://doi.org/10.3390/e21080725 - 25 Jul 2019
Abstract
We present a thermodynamic framework for the refined weak coupling limit. In this limit, the interaction between system and environment is weak, but not negligible. As a result, the system dynamics becomes non-Markovian breaking divisibility conditions. Nevertheless, we propose a derivation of the [...] Read more.
We present a thermodynamic framework for the refined weak coupling limit. In this limit, the interaction between system and environment is weak, but not negligible. As a result, the system dynamics becomes non-Markovian breaking divisibility conditions. Nevertheless, we propose a derivation of the first and second law just in terms of the reduced system dynamics. To this end, we extend the refined weak coupling limit for allowing slowly-varying external drivings and reconsider the definition of internal energy due to the non-negligible interaction. Full article
(This article belongs to the Special Issue Quantum Entropies and Complexity)
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Open AccessArticle
Quantum Features of Macroscopic Fields: Entropy and Dynamics
Entropy 2019, 21(7), 705; https://doi.org/10.3390/e21070705 - 18 Jul 2019
Abstract
Macroscopic fields such as electromagnetic, magnetohydrodynamic, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random [...] Read more.
Macroscopic fields such as electromagnetic, magnetohydrodynamic, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of the field combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equation for the reduced state of the field is obtained by reduction of the generalized quasi-free dynamical semigroups describing irreversible evolution of bosonic quantum field and the definition of entropy for the reduced state of the field follows from the von Neumann entropy of quantum field states. The presented formalism can be applied, for example, to superradiance phenomena and allows unifying the Mueller and Jones calculi in polarization optics. Full article
(This article belongs to the Special Issue Quantum Entropies and Complexity)
Open AccessArticle
Canonical Divergence for Measuring Classical and Quantum Complexity
Entropy 2019, 21(4), 435; https://doi.org/10.3390/e21040435 - 24 Apr 2019
Cited by 1
Abstract
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both classical and quantum systems. On the simplex of probability measures, it is proved that the new divergence coincides with the Kullback–Leibler divergence, which is used to quantify [...] Read more.
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both classical and quantum systems. On the simplex of probability measures, it is proved that the new divergence coincides with the Kullback–Leibler divergence, which is used to quantify how much a probability measure deviates from the non-interacting states that are modeled by exponential families of probabilities. On the space of positive density operators, we prove that the same divergence reduces to the quantum relative entropy, which quantifies many-party correlations of a quantum state from a Gibbs family. Full article
(This article belongs to the Special Issue Quantum Entropies and Complexity)
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