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Quantum Information Entropy in Physics

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

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 3715

Special Issue Editor


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Guest Editor
"Gleb Wataghin" Institute of Physics, University of Campinas, Campinas 13083-859, SP, Brazil
Interests: cavity quantum electrodynamics; quantum cryptography; trapped ion dynamics; quantum effects; decoherence

Special Issue Information

Dear Colleagues,

Shannon’s quantification of the concept of “information” was an essential step towards its understanding, whilst also attempting to provide an answer to the following question: what is the best way of encoding a message to be transmitted? For that, he introduced the quantity known as “information entropy”, usually denoted as H. Interestingly, H, which plays a key role in the information theory, bears an analogy with entropy in statistical mechanics, having the same functional form. Following this path, Jaynes established a connection between these two quantities, bringing together the worlds of information theory and thermodynamics. Subsequently, the works of Gordon, Helstrom, Stratonovich and Holevo considered the possibility of encoding information in quantum states; thus, creating the “quantum information theory”. It became clear that entropy is also an essential concept in the quantum domain, with the entropy introduced by von Neumann being the quantum analogue of H. Additionally, Umegaki proposed a quantum generalization of the Kullback–Leibler relative entropy, known as the quantum relative entropy, from which one can derive other forms of quantum entropies. In general, quantum information entropy has become an important tool to quantify characteristic quantum properties, e.g., quantum correlations, quantum coherence as well as the non-Gaussianity of quantum states. This has been accompanied by substantial progress in the fields of quantum information processing, quantum communications and quantum sensing, the backbones of quantum technologies.

In this Special Issue, we wish to accept unpublished contributions, either original or reviews, related to the theme of quantum information entropy in physics. This is a broad topic ranging from application-oriented subjects such as quantum communications and quantum computing to developments in fundamental physics, quantum thermodynamics, quantum information in many-body systems, etc.

Prof. Dr. Antonio Vidiella-Barrranco
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 entropy
  • quantum information processing
  • quantum entanglement
  • quantum coherence
  • quantum computing
  • quantum key distribution
  • quantum thermodynamics
  • quantum optics

Published Papers (2 papers)

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15 pages, 432 KiB  
Article
Non-Hermitian Generalization of Rényi Entropy
by Daili Li and Chao Zheng
Entropy 2022, 24(11), 1563; https://doi.org/10.3390/e24111563 - 30 Oct 2022
Cited by 7 | Viewed by 1641
Abstract
From their conception to present times, different concepts and definitions of entropy take key roles in a variety of areas from thermodynamics to information science, and they can be applied to both classical and quantum systems. Among them is the Rényi entropy. It [...] Read more.
From their conception to present times, different concepts and definitions of entropy take key roles in a variety of areas from thermodynamics to information science, and they can be applied to both classical and quantum systems. Among them is the Rényi entropy. It is able to characterize various properties of classical information with a unified concise form. We focus on the quantum counterpart, which unifies the von Neumann entropy, max- and min-entropy, collision entropy, etc. It can only be directly applied to Hermitian systems because it usually requires that the density matrices is normalized. For a non-Hermitian system, the evolved density matrix may not be normalized; i.e., the trace can be larger or less than one as the time evolution. However, it is not well-defined for the Rényi entropy with a non-normalized probability distribution relevant to the density matrix of a non-Hermitian system, especially when the trace of the non-normalized density matrix is larger than one. In this work, we investigate how to describe the Rényi entropy for non-Hermitian systems more appropriately. We obtain a concisely and generalized form of α-Rényi entropy, which we extend the unified order-α from finite positive real numbers to zero and infinity. Our generalized α-Rényi entropy can be directly calculated using both of the normalized and non-normalized density matrices so that it is able to describe non-Hermitian entropy dynamics. We illustrate the necessity of our generalization by showing the differences between ours and the conventional Rényi entropy for non-Hermitian detuning two-level systems. Full article
(This article belongs to the Special Issue Quantum Information Entropy in Physics)
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20 pages, 894 KiB  
Article
Quantum Statistical Complexity Measure as a Signaling of Correlation Transitions
by André T. Cesário, Diego L. B. Ferreira, Tiago Debarba, Fernando Iemini, Thiago O. Maciel and Reinaldo O. Vianna
Entropy 2022, 24(8), 1161; https://doi.org/10.3390/e24081161 - 19 Aug 2022
Viewed by 1467
Abstract
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signaling function of quantum order–disorder transitions. We discuss the possibility for such transitions to characterize interesting physical phenomena, as quantum phase [...] Read more.
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signaling function of quantum order–disorder transitions. We discuss the possibility for such transitions to characterize interesting physical phenomena, as quantum phase transitions, or abrupt variations in correlation distributions. We apply our measure on two exactly solvable Hamiltonian models: the 1D-Quantum Ising Model (in the single-particle reduced state), and on Heisenberg XXZ spin-1/2 chain (in the two-particle reduced state). We analyze its behavior across quantum phase transitions for finite system sizes, as well as in the thermodynamic limit by using Bethe Ansatz technique. Full article
(This article belongs to the Special Issue Quantum Information Entropy in Physics)
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