Mathematics

Research

15 pages, 492 KiB

Open AccessArticle

Correlations in Quantum Network Topologies Created with Cloning

by Manish Kumar Shukla, Minyi Huang, Indranil Chakrabarty and Junde Wu

Mathematics 2023, 11(11), 2440; https://doi.org/10.3390/math11112440 - 25 May 2023

Cited by 1 | Viewed by 889

With progress in quantum technologies, the field of quantum networks has emerged as an important area of research. In the last few years, there has been substantial progress in understanding the correlations present in quantum networks. In this article, we study cloning as [...] Read more.

With progress in quantum technologies, the field of quantum networks has emerged as an important area of research. In the last few years, there has been substantial progress in understanding the correlations present in quantum networks. In this article, we study cloning as a prospective method to generate three party quantum networks which will help us to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in situations wherever the availability of entangled pairs is limited. In addition to that, we focus on the problem of distinguishing networks created by cloning from those that are created by distributing independently generated entangled pairs. We find that there are several states that cannot be distinguished using the Finner inequalities in the standard way. For such states, we propose an extension to the existing Finner inequality for triangle networks by further increasing the number of observers from three to four or six depending on the network topology. This takes into account the additional correlations that exist in the case of cloned networks. In the last part of the article, we use tripartite mutual information to distinguish cloned networks from networks created by independent sources and further use squashed entanglement as a measure to quantify the amount of dependence in the cloned networks. Full article

(This article belongs to the Special Issue Quantum Algorithms and Relative Problems)

► Show Figures

Figure 1

10 pages, 305 KiB

Open AccessArticle

Tighter Monogamy Relations for Concurrence and Negativity in Multiqubit Systems

by Yuan-Hong Tao, Kai Zheng, Zhi-Xiang Jin and Shao-Ming Fei

Mathematics 2023, 11(5), 1159; https://doi.org/10.3390/math11051159 - 26 Feb 2023

Cited by 4 | Viewed by 1295

Abstract

The entanglement in multipartite quantum system is hard to characterize and quantify, although it has been intensively studied in bipartite systems. The monogamy of entanglement, as a special property of multipartite systems, shows the distribution of entanglement in the system. In this paper, [...] Read more.

The entanglement in multipartite quantum system is hard to characterize and quantify, although it has been intensively studied in bipartite systems. The monogamy of entanglement, as a special property of multipartite systems, shows the distribution of entanglement in the system. In this paper, we investigate the monogamy relations for multi-qubit systems. By using two entangled measures, namely the concurrence C and the negativity

N_{c}

, we establish tighter monogamy inequalities for their

α

-th power than those in all the existing ones. We also illustrate the tightness of our results for some classes of quantum states. Full article

(This article belongs to the Special Issue Quantum Algorithms and Relative Problems)

► Show Figures

Figure 1

30 pages, 4361 KiB

Open AccessArticle

Binary Approaches of Quantum-Based Avian Navigation Optimizer to Select Effective Features from High-Dimensional Medical Data

by Mohammad H. Nadimi-Shahraki, Ali Fatahi, Hoda Zamani and Seyedali Mirjalili

Mathematics 2022, 10(15), 2770; https://doi.org/10.3390/math10152770 - 4 Aug 2022

Cited by 38 | Viewed by 2235

Abstract

Many metaheuristic approaches have been developed to select effective features from different medical datasets in a feasible time. However, most of them cannot scale well to large medical datasets, where they fail to maximize the classification accuracy and simultaneously minimize the number of [...] Read more.

Many metaheuristic approaches have been developed to select effective features from different medical datasets in a feasible time. However, most of them cannot scale well to large medical datasets, where they fail to maximize the classification accuracy and simultaneously minimize the number of selected features. Therefore, this paper is devoted to developing an efficient binary version of the quantum-based avian navigation optimizer algorithm (QANA) named BQANA, utilizing the scalability of the QANA to effectively select the optimal feature subset from high-dimensional medical datasets using two different approaches. In the first approach, several binary versions of the QANA are developed using S-shaped, V-shaped, U-shaped, Z-shaped, and quadratic transfer functions to map the continuous solutions of the canonical QANA to binary ones. In the second approach, the QANA is mapped to binary space by converting each variable to 0 or 1 using a threshold. To evaluate the proposed algorithm, first, all binary versions of the QANA are assessed on different medical datasets with varied feature sizes, including Pima, HeartEW, Lymphography, SPECT Heart, PenglungEW, Parkinson, Colon, SRBCT, Leukemia, and Prostate tumor. The results show that the BQANA developed by the second approach is superior to other binary versions of the QANA to find the optimal feature subset from the medical datasets. Then, the BQANA was compared with nine well-known binary metaheuristic algorithms, and the results were statistically assessed using the Friedman test. The experimental and statistical results demonstrate that the proposed BQANA has merit for feature selection from medical datasets. Full article

(This article belongs to the Special Issue Quantum Algorithms and Relative Problems)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Quantum Algorithms and Relative Problems

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (3 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI