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Entropy
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Quantum Entropies and Complexity
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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 (29 February 2020) | Viewed by 21864

Special Issue Editor

Dr. Fabio Benatti

E-Mail Website
Guest Editor
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 submissions that pass pre-check are 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 2600 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

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Published Papers (6 papers)

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Research

29 pages, 4801 KiB  
Article
Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well
by Frank Schäfer, Miguel A. Bastarrachea-Magnani, Axel U. J. Lode, Laurent de Forges de Parny and Andreas Buchleitner
Entropy 2020, 22(4), 382; https://doi.org/10.3390/e22040382 - 26 Mar 2020
Cited by 4 | Viewed by 4308
Abstract
We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behavior [...] Read more.
We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behavior of the particles launched either at the single-particle ground state or saddle-point energy, in a time-independent potential. We complement these results by a characterization of the cross-over from diabatic to quasi-adiabatic evolution under finite-time switching of the potential barrier, via the associated time evolution of a single particle’s von Neumann entropy. This is achieved with the help of the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X)—which also allows us to extrapolate our results for increasing particle numbers. Full article
(This article belongs to the Special Issue Quantum Entropies and Complexity)
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7 pages, 1590 KiB  
Article
Experimentally Demonstrate the Spin-1 Information Entropic Inequality Based on Simulated Photonic Qutrit States
by Lianzhen Cao, Xia Liu, Yang Yang, Qinwei Zhang, Jiaqiang Zhao and Huaixin Lu
Entropy 2020, 22(2), 219; https://doi.org/10.3390/e22020219 - 15 Feb 2020
Viewed by 2487
Abstract
Quantum correlations of higher-dimensional systems are an important content of quantum information theory and quantum information application. The quantification of quantum correlation of high-dimensional quantum systems is crucial, but difficult. In this paper, using the second-order nonlinear optical effect and multiphoton interference enhancement [...] Read more.
Quantum correlations of higher-dimensional systems are an important content of quantum information theory and quantum information application. The quantification of quantum correlation of high-dimensional quantum systems is crucial, but difficult. In this paper, using the second-order nonlinear optical effect and multiphoton interference enhancement effect, we experimentally implement the photonic qutrit states and demonstrate the spin-1 information entropic inequality for the first time to quantitative quantum correlation. Our work shows that information entropy is an important way to quantify quantum correlation and quantum information processing. Full article
(This article belongs to the Special Issue Quantum Entropies and Complexity)
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20 pages, 893 KiB  
Article
Quasi-Entropies and Non-Markovianity
by Fabio Benatti and Luigi Brancati
Entropy 2019, 21(10), 1020; https://doi.org/10.3390/e21101020 - 21 Oct 2019
Cited by 2 | Viewed by 3675
Abstract
We address an informational puzzle that appears with a non-Markovian open qubit dynamics: namely the fact that, while, according to the existing witnesses of information flows, a single qubit affected by that dissipative dynamics does not show information returning to it from its [...] Read more.
We address an informational puzzle that appears with a non-Markovian open qubit dynamics: namely the fact that, while, according to the existing witnesses of information flows, a single qubit affected by that dissipative dynamics does not show information returning to it from its environment, instead two qubits do show such information when evolving independently under the same dynamics. We solve the puzzle by adding the so-called quasi-entropies to the possible witnesses of information flows. Full article
(This article belongs to the Special Issue Quantum Entropies and Complexity)
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20 pages, 513 KiB  
Article
Quantum Thermodynamics in the Refined Weak Coupling Limit
by Ángel Rivas
Entropy 2019, 21(8), 725; https://doi.org/10.3390/e21080725 - 25 Jul 2019
Cited by 14 | Viewed by 3707
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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13 pages, 269 KiB  
Article
Quantum Features of Macroscopic Fields: Entropy and Dynamics
by Robert Alicki
Entropy 2019, 21(7), 705; https://doi.org/10.3390/e21070705 - 18 Jul 2019
Cited by 5 | Viewed by 3688
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)
13 pages, 312 KiB  
Article
Canonical Divergence for Measuring Classical and Quantum Complexity
by Domenico Felice, Stefano Mancini and Nihat Ay
Entropy 2019, 21(4), 435; https://doi.org/10.3390/e21040435 - 24 Apr 2019
Cited by 8 | Viewed by 3321
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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