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Entropy
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Quantum Shannon Theory and Its Applications
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Quantum Shannon Theory and Its Applications

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

Deadline for manuscript submissions: closed (15 November 2023) | Viewed by 4479

Special Issue Editors

Dr. Kabgyun Jeong

E-Mail Website
Guest Editor
1. Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea
2. School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
Interests: private quantum channel; quantum channel capacities including entropy power inequality; concentration of measure phenomena in quantum information
Prof. Dr. Jaewan Kim

E-Mail Website
Guest Editor
School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
Interests: quantum; information theory, quantum computing; quantum algorithm; fundamentals of quantum physics

Special Issue Information

Dear Colleagues,

Quantum Shannon theory is a branch of quantum information theory that extends the classical Shannon theory to quantum systems. It is based on unique effects that only occur in quantum systems, such as superposition and entanglement. Its significance lies in providing a mathematical framework for information transfer in quantum systems, and its research results have influenced adjacent fields, such as mathematics, theoretical physics, quantum information science, and computer and computational science. Recently, research on key components of the quantum internet, such as secure quantum cryptography protocols, quantum channel capacity, and coding theory for quantum networks, has been actively pursued, and the results of quantum Shannon theory are expected to have a significant impact on the construction of a quantum internet.

This Special Issue will accept submissions on but not limited to the following research areas:

  • Superactivation of quantum channel capacities;
  • Algorithmic decidability of quantum channel problems;
  • Quantum MIMO communication schemes;
  • Entanglement-based quantum key distribution;
  • Trainability of quantum neural networks using quantum Shannon theory;
  • Coding theories for quantum networks.

Dr. Kabgyun Jeong
Prof. Dr. Jaewan Kim
Guest Editors

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 (conditional)-mutual information
  • quantum entropy inequalities
  • quantum channel capacities
  • quantum network
  • quantum state redistribution
  • quantum error correction
  • quantum state tomography
  • quantum internet
  • resource theory of entanglement
  • quantum asymptotic equipartition property

Published Papers (4 papers)

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Research

11 pages, 360 KiB  
Article
Entanglement of Temporal Sections as Quantum Histories and Their Quantum Correlation Bounds
by Marcin Nowakowski
Entropy 2024, 26(3), 198; https://doi.org/10.3390/e26030198 - 26 Feb 2024
Viewed by 887
Abstract
In this paper, we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiates them from spatial quantum correlations. With a growing interest in the representation of quantum states as topological objects, we consider quantum history bundles [...] Read more.
In this paper, we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiates them from spatial quantum correlations. With a growing interest in the representation of quantum states as topological objects, we consider quantum history bundles based on the temporal manifold and show the source of the violation of monogamous temporal Bell-like inequalities. We introduce definitions for the mixture of quantum histories and consider their entanglement as sections over the Hilbert vector bundles. As a generalization of temporal Bell-like inequalities, we derive the quantum bound for multi-time Bell-like inequalities. Full article
(This article belongs to the Special Issue Quantum Shannon Theory and Its Applications)
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24 pages, 407 KiB  
Article
Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes
by Jianzhang Chen, Wanchuan Fang, Shuo Zhou, Jie Qiu, Chenyang Zhang, Yixin Xu, Bozhe Zeng and Youqin Chen
Entropy 2023, 25(12), 1603; https://doi.org/10.3390/e25121603 - 30 Nov 2023
Viewed by 921
Abstract
Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted through asymmetric channels. Currently, a significant body of [...] Read more.
Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted through asymmetric channels. Currently, a significant body of literature has investigated the construction of asymmetric QEC codes. However, the asymmetry of most QEC codes identified in the literature is limited by the dual-containing condition within the Calderbank-Shor-Steane (CSS) framework. This limitation restricts the exploration of their full potential in terms of asymmetry. In order to enhance the asymmetry of asymmetric QEC codes, we utilize entanglement-assisted technology and exploit the algebraic structure of cyclotomic cosets of constacyclic codes to achieve this goal. In this paper, we generalize the decomposition method of the defining set for constacyclic codes and apply it to count the number of pre-shared entangled states in order to construct four new classes of asymmetric entanglement-assisted quantum maximal-distance separable (EAQMDS) codes that satisfy the asymmetric entanglement-assisted quantum Singleton bound. Compared with the codes existing in the literature, the lengths of the constructed EAQMDS codes and the number of pre-shared entangled states are more general, and the codes constructed in this paper have greater asymmetry. Full article
(This article belongs to the Special Issue Quantum Shannon Theory and Its Applications)
12 pages, 1218 KiB  
Article
Quantum Information Entropy for Another Class of New Proposed Hyperbolic Potentials
by R. Santana-Carrillo, Roberto de J. León-Montiel, Guo-Hua Sun and Shi-Hai Dong
Entropy 2023, 25(9), 1296; https://doi.org/10.3390/e25091296 - 5 Sep 2023
Viewed by 885
Abstract
In this work, we investigate the Shannon entropy of four recently proposed hyperbolic potentials through studying position and momentum entropies. Our analysis reveals that the wave functions of the single-well potentials U0,3 exhibit greater localization compared to the double-well potentials [...] Read more.
In this work, we investigate the Shannon entropy of four recently proposed hyperbolic potentials through studying position and momentum entropies. Our analysis reveals that the wave functions of the single-well potentials U0,3 exhibit greater localization compared to the double-well potentials U1,2. This difference in localization arises from the depths of the single- and double-well potentials. Specifically, we observe that the position entropy density shows higher localization for the single-well potentials, while their momentum probability density becomes more delocalized. Conversely, the double-well potentials demonstrate the opposite behavior, with position entropy density being less localized and momentum probability density showing increased localization. Notably, our study also involves examining the Bialynicki–Birula and Mycielski (BBM) inequality, where we find that the Shannon entropies still satisfy this inequality for varying depths u¯. An intriguing observation is that the sum of position and momentum entropies increases with the variable u¯ for potentials U1,2,3, while for U0, the sum decreases with u¯. Additionally, the sum of the cases U0 and U3 almost remains constant within the relative value 0.01 as u¯ increases. Our study provides valuable insights into the Shannon entropy behavior for these hyperbolic potentials, shedding light on their localization characteristics and their relation to the potential depths. Finally, we extend our analysis to the Fisher entropy F¯x and find that it increases with the depth u¯ of the potential wells but F¯p decreases with the depth. Full article
(This article belongs to the Special Issue Quantum Shannon Theory and Its Applications)
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12 pages, 283 KiB  
Article
The Necessary and Sufficient Conditions When Global and Local Fidelities Are Equal
by Seong-Kun Kim and Yonghae Lee
Entropy 2023, 25(7), 1093; https://doi.org/10.3390/e25071093 - 21 Jul 2023
Viewed by 940
Abstract
In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system A⊗B is always less [...] Read more.
In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system A⊗B is always less than or equal to the quantum fidelity between the states in subsystem A alone. While this fidelity inequality is well understood, determining the conditions under which the inequality becomes an equality remains an open question. In this paper, we present the necessary and sufficient conditions for the equality of fidelities between a bipartite system A⊗B and subsystem A, considering pure quantum states. Moreover, we provide explicit representations of quantum states that satisfy the fidelity equality, based on our derived results. Full article
(This article belongs to the Special Issue Quantum Shannon Theory and Its Applications)
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