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Entropy
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Classical and Quantum Networks: Theory, Modeling and Optimization
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Classical and Quantum Networks: Theory, Modeling and Optimization

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

Deadline for manuscript submissions: closed (17 January 2025) | Viewed by 13436

Special Issue Editors

Dr. Avishy Carmi

E-Mail Website
Guest Editor
Center for Quantum Information Science and Tech-nology, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer Sheva, Israel
Interests: classical and quantum information processing; quantum nonlocality; estimation theory; filtering theory; information processing; complex and multi-agent systems; natural; quantum and unconventional computation
Special Issues, Collections and Topics in MDPI journals
Dr. Eliahu Cohen

E-Mail Website
Guest Editor
Faculty of Engineering, Institute for Nanotechnology & Advanced Materials, and Center for Quantum Entanglement Science & Technology, Bar-Ilan University, Ramat-Gan 5290002, Israel
Interests: quantum mechanics; quantum information; quantum optics; quantum field theory
Special Issues, Collections and Topics in MDPI journals
Dr. Dana Ben Porath

E-Mail Website
Guest Editor
Faculty of Engineering, Institute for Nanotechnology & Advanced Materials, and Center for Quantum Entanglement Science & Technology, Bar-Ilan University, Ramat-Gan 5290002, Israel
Interests: statistical physics; network theory; percolation theory; quantum information

Special Issue Information

Dear Colleagues,

Network theory, both classical and quantum, has proved highly fruitful for analyzing a variety of problems. The formulation in terms of networks is often general and abstract, which allows it to fit into multiple different contexts. For example, the same tools from classical network science and percolation theory are applicable in the analysis of the resiliency of a complex system and, likewise, in the spread of an epidemic [1,2]. In this Special Issue, we will focus on generalizations and applications of classical networks to quantum systems, as well as on unique quantum constructions. The reported studies may relate to various areas, ranging from fundamental explorations of quantum nonlocality [3-5] to applications for quantum communications [6-9].

References:

[1] Newman, M. E. (2002). Spread of epidemic disease on networks. Physical review E, 66(1), 016128.

[2] Cohen, R., & Havlin, S. (2010). Complex networks: structure, robustness and function. Cambridge university press.

[3] Perseguers, S., Lapeyre, G. J., Cavalcanti, D., Lewenstein, M., & Acín, A. (2013). Distribution of entanglement in large-scale quantum networks. Reports on Progress in Physics, 76(9), 096001.

[4] Pozas-Kerstjens, A., Gisin, N., & Tavakoli, A. (2022). Full network nonlocality. Physical review letters, 128(1), 010403.

[5] Peled, B. Y., Te'eni, A., Cohen, E., & Carmi, A. (2021). Population dynamics of entangled species. arXiv preprint arXiv:2109.04237.

[6] Duan, L. M., & Monroe, C. (2010). Colloquium: Quantum networks with trapped ions. Reviews of Modern Physics, 82(2), 120.

[7] Kozlowski, W., & Wehner, S. (2019, September). Towards large-scale quantum networks. In Proceedings of the Sixth Annual ACM International Conference on Nanoscale Computing and Communication (pp. 1-7).

[8] Zhuang, Q., & Zhang, B. (2021). Quantum communication capacity transition of complex quantum networks. Physical Review A, 104(2), 022608.

[9] Meng, X., Gao, J., & Havlin, S. (2021). Concurrence percolation in quantum networks. Physical Review Letters, 126(17), 170501.

Dr. Avishy Carmi
Dr. Eliahu Cohen
Dr. Dana Ben Porath
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

  • network dynamics
  • network topology
  • complex networks
  • percolation
  • quantum entanglement
  • quantum correlations
  • quantum interconnect
  • quantum walks
  • quantum key distribution

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Related Special Issue

Published Papers (7 papers)

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Research

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28 pages, 2754 KiB  
Article
Exploring Quantum Neural Networks for Demand Forecasting
by Gleydson Fernandes de Jesus, Maria Heloísa Fraga da Silva, Otto Menegasso Pires, Lucas Cruz da Silva, Clebson dos Santos Cruz and Valéria Loureiro da Silva
Entropy 2025, 27(5), 490; https://doi.org/10.3390/e27050490 - 1 May 2025
Viewed by 177
Abstract
Forecasting demand for assets and services can be addressed in various markets, providing a competitive advantage when the predictive models used demonstrate high accuracy. However, the training of machine learning models incurs high computational costs, which may limit the training of prediction models [...] Read more.
Forecasting demand for assets and services can be addressed in various markets, providing a competitive advantage when the predictive models used demonstrate high accuracy. However, the training of machine learning models incurs high computational costs, which may limit the training of prediction models based on available computational capacity. In this context, this paper presents an approach for training demand prediction models using quantum neural networks. For this purpose, a quantum neural network was used to forecast demand for vehicle financing. A classical recurrent neural network was used to compare the results, and they show a similar predictive capacity between the classical and quantum models, with the advantage of using a lower number of training parameters and also converging in fewer steps. Utilizing quantum computing techniques offers a promising solution to overcome the limitations of traditional machine learning approaches in training predictive models for complex market dynamics. Full article
(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)
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14 pages, 653 KiB  
Article
A Consistent Approach to Modeling Quantum Observers
by David W. Ring
Entropy 2025, 27(3), 302; https://doi.org/10.3390/e27030302 - 14 Mar 2025
Viewed by 476
Abstract
A number of no-go theorems have shown that Wigner’s Friend scenarios combined with various metaphysical assumptions lead to contradictions in any version of quantum theory. We present an alternative constructive approach that only assumes that agents make properly qualified true statements. Quantum observers [...] Read more.
A number of no-go theorems have shown that Wigner’s Friend scenarios combined with various metaphysical assumptions lead to contradictions in any version of quantum theory. We present an alternative constructive approach that only assumes that agents make properly qualified true statements. Quantum observers are modeled rigorously, although simplistically, using quantum circuits. Terminology is suggested to help avoid contradictions. Our methodology is applied to the Frauchiger-Renner paradox and results in statements by all agents that are both true and consistent. Quantum theory evades the no-go theorems because they make an incorrect implicit assumption about how quantum agents behave. Full article
(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)
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26 pages, 481 KiB  
Article
Controlled Double-Direction Cyclic Quantum Communication of Arbitrary Two-Particle States
by Nueraminaimu Maihemuti, Zhanheng Chen, Jiayin Peng, Yimamujiang Aisan and Jiangang Tang
Entropy 2025, 27(3), 292; https://doi.org/10.3390/e27030292 - 11 Mar 2025
Viewed by 555
Abstract
With the rapid development of quantum communication technologies, controlled double-direction cyclic (CDDC) quantum communication has become an important research direction. However, how to choose an appropriate quantum state as a channel to achieve double-direction cyclic (DDC) quantum communication for multi-particle entangled states remains [...] Read more.
With the rapid development of quantum communication technologies, controlled double-direction cyclic (CDDC) quantum communication has become an important research direction. However, how to choose an appropriate quantum state as a channel to achieve double-direction cyclic (DDC) quantum communication for multi-particle entangled states remains an unresolved challenge. This study aims to address this issue by constructing a suitable quantum channel and investigating the DDC quantum communication of two-particle states. Initially, we create a 25-particle entangled state using Hadamard and controlled-NOT (CNOT) gates, and provide its corresponding quantum circuit implementation. Based on this entangled state as a quantum channel, we propose two new four-party CDDC schemes, applied to quantum teleportation (QT) and remote state preparation (RSP), respectively. In both schemes, each communicating party can synchronously transmit two different arbitrary two-particle states to the other parties under supervisory control, achieving controlled quantum cyclic communication in both clockwise and counterclockwise directions. Additionally, the presented two schemes of four-party CDDC quantum communication are extended to situations where n>3 communicating parties. In each proposed scheme, we provide universal analytical formulas for the local operations of the sender, supervisor, and receiver, demonstrating that the success probability of each scheme can reach 100%. These schemes only require specific two-particle projective measurements, single-particle von Neumann measurements, and Pauli gate operations, all of which can be implemented with current technologies. We have also evaluated the inherent efficiency, security, and control capabilities of the proposed schemes. In comparison to earlier methods, the results demonstrate that our schemes perform exceptionally well. This study provides a theoretical foundation for bidirectional controlled quantum communication of multi-particle states, aiming to enhance security and capacity while meeting the diverse needs of future network scenarios. Full article
(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)
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17 pages, 1001 KiB  
Article
Enhanced Coexistence of Quantum Key Distribution and Classical Communication over Hollow-Core and Multi-Core Fibers
by Weiwen Kong, Yongmei Sun, Tianqi Dou, Yuheng Xie, Zhenhua Li, Yaoxian Gao, Qi Zhao, Na Chen, Wenpeng Gao, Yuanchen Hao, Peizhe Han, Yang Liu and Jianjun Tang
Entropy 2024, 26(7), 601; https://doi.org/10.3390/e26070601 - 15 Jul 2024
Cited by 2 | Viewed by 2136
Abstract
In this paper, we investigate the impact of classical optical communications in quantum key distribution (QKD) over hollow-core fiber (HCF), multi-core fiber (MCF) and single-core fiber (SCF) and propose wavelength allocation schemes to enhance QKD performance. Firstly, we theoretically analyze noise interference in [...] Read more.
In this paper, we investigate the impact of classical optical communications in quantum key distribution (QKD) over hollow-core fiber (HCF), multi-core fiber (MCF) and single-core fiber (SCF) and propose wavelength allocation schemes to enhance QKD performance. Firstly, we theoretically analyze noise interference in QKD over HCF, MCF and SCF, such as spontaneous Raman scattering (SpRS) and four-wave mixing (FWM). To mitigate these noise types and optimize QKD performance, we propose a joint noise suppression wavelength allocation (JSWA) scheme. FWM noise suppression wavelength allocation and Raman noise suppression wavelength allocation are also proposed for comparison. The JSWA scheme indicates a significant enhancement in extending the simultaneous transmission distance of classical signals and QKD, reaching approximately 100 km in HCF and 165 km in MCF under a classical power per channel of 10 dBm. Therefore, MCF offers a longer secure transmission distance compared with HCF when classical signals and QKD coexist in the C-band. However, when classical signals are in the C-band and QKD operates in the O-band, the performance of QKD in HCF surpasses that in MCF. This research establishes technical foundations for the design and deployment of QKD optical networks. Full article
(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)
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22 pages, 7161 KiB  
Article
Discrete-Time Quantum Walk on Multilayer Networks
by Mahesh N. Jayakody, Priodyuti Pradhan, Dana Ben Porath and Eliahu Cohen
Entropy 2023, 25(12), 1610; https://doi.org/10.3390/e25121610 - 30 Nov 2023
Cited by 2 | Viewed by 1845
Abstract
A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a [...] Read more.
A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a recurrence formula for the coefficients of the wave function of a quantum walker on an undirected graph with a finite number of nodes. By extending this formula to include extra layers, we develop a simulation model to describe the time evolution of the quantum walker on a multilayer network. The time-averaged probability and the return probability of the quantum walker are studied with Fourier, and Grover walks on multilayer networks. Furthermore, we analyze the impact of decoherence on quantum transport, shedding light on how environmental interactions may impact the behavior of quantum walkers on multilayer network structures. Full article
(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)
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15 pages, 2580 KiB  
Article
Cost-Optimization-Based Quantum Key Distribution over Quantum Key Pool Optical Networks
by Jie Jia, Bowen Dong, Le Kang, Huanwen Xie and Banghong Guo
Entropy 2023, 25(4), 661; https://doi.org/10.3390/e25040661 - 14 Apr 2023
Cited by 4 | Viewed by 2659
Abstract
The Measurement-Device-Independent-Quantum Key Distribution (MDI-QKD) has the advantage of extending the secure transmission distances. The MDI-QKD combined with the Hybrid-Trusted and Untrusted Relay (HTUR) is used to deploy large-scale QKD networks, which effectively saves deployment cost. We propose an improved scheme for the [...] Read more.
The Measurement-Device-Independent-Quantum Key Distribution (MDI-QKD) has the advantage of extending the secure transmission distances. The MDI-QKD combined with the Hybrid-Trusted and Untrusted Relay (HTUR) is used to deploy large-scale QKD networks, which effectively saves deployment cost. We propose an improved scheme for the QKD network architecture and cost analysis, which simplifies the number of QKD transmitters and incorporates the quantum key pool (QKP) in the QKD network. We developed a novel Hybrid-QKD-Network-Cost (HQNC) heuristic algorithm to solve the cost optimization problem. Simulations verified that the scheme in this paper could save the cost by over 50 percent and 90 percent, respectively. Full article
(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)
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Review

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37 pages, 1823 KiB  
Review
Percolation Theories for Quantum Networks
by Xiangyi Meng, Xinqi Hu, Yu Tian, Gaogao Dong, Renaud Lambiotte, Jianxi Gao and Shlomo Havlin
Entropy 2023, 25(11), 1564; https://doi.org/10.3390/e25111564 - 20 Nov 2023
Cited by 9 | Viewed by 4260
Abstract
Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively [...] Read more.
Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network’s indirect connectivity. This realization leads to the emergence of an alternative theory called “concurrence percolation”, which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design. Full article
(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)
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