Exploring the Percolation Phenomena in Quantum Networks
Quantum entanglement as a non-local correlation between particles is critical to the transmission of quantum information in quantum networks (QNs); the key challenge lies in establishing long-distance entanglement transmission between distant targets. This issue aligns with percolation theory, and a...
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MDPI AG
2024-11-01
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| author | Chuanxin Wang Xinqi Hu Gaogao Dong |
| author_facet | Chuanxin Wang Xinqi Hu Gaogao Dong |
| author_sort | Chuanxin Wang |
| collection | DOAJ |
| description | Quantum entanglement as a non-local correlation between particles is critical to the transmission of quantum information in quantum networks (QNs); the key challenge lies in establishing long-distance entanglement transmission between distant targets. This issue aligns with percolation theory, and as a result, an entanglement distribution scheme called “Classical Entanglement Percolation” (CEP) has been proposed. While this scheme provides an effective framework, “Quantum Entanglement Percolation” (QEP) indicates a lower percolation threshold through quantum preprocessing strategies, which will modify the network topology. Meanwhile, an emerging statistical theory known as “Concurrence Percolation” reveals the unique advantages of quantum networks, enabling entanglement transmission under lower conditions. It fundamentally belongs to a different universality class from classical percolation. Although these studies have made significant theoretical advancements, most are based on an idealized pure state network model. In practical applications, quantum states are often affected by thermal noise, resulting in mixed states. When these mixed states meet specific conditions, they can be transformed into pure states through quantum operations and further converted into singlets with a certain probability, thereby facilitating entanglement percolation in mixed state networks. This finding greatly broadens the application prospects of quantum networks. This review offers a comprehensive overview of the fundamental theories of quantum percolation and the latest cutting-edge research developments. |
| format | Article |
| id | doaj-art-3bea83601e6b4c55bb05ffaa0b58e93a |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-3bea83601e6b4c55bb05ffaa0b58e93a2024-11-26T18:11:51ZengMDPI AGMathematics2227-73902024-11-011222356810.3390/math12223568Exploring the Percolation Phenomena in Quantum NetworksChuanxin Wang0Xinqi Hu1Gaogao Dong2School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, ChinaSchool of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, ChinaSchool of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, ChinaQuantum entanglement as a non-local correlation between particles is critical to the transmission of quantum information in quantum networks (QNs); the key challenge lies in establishing long-distance entanglement transmission between distant targets. This issue aligns with percolation theory, and as a result, an entanglement distribution scheme called “Classical Entanglement Percolation” (CEP) has been proposed. While this scheme provides an effective framework, “Quantum Entanglement Percolation” (QEP) indicates a lower percolation threshold through quantum preprocessing strategies, which will modify the network topology. Meanwhile, an emerging statistical theory known as “Concurrence Percolation” reveals the unique advantages of quantum networks, enabling entanglement transmission under lower conditions. It fundamentally belongs to a different universality class from classical percolation. Although these studies have made significant theoretical advancements, most are based on an idealized pure state network model. In practical applications, quantum states are often affected by thermal noise, resulting in mixed states. When these mixed states meet specific conditions, they can be transformed into pure states through quantum operations and further converted into singlets with a certain probability, thereby facilitating entanglement percolation in mixed state networks. This finding greatly broadens the application prospects of quantum networks. This review offers a comprehensive overview of the fundamental theories of quantum percolation and the latest cutting-edge research developments.https://www.mdpi.com/2227-7390/12/22/3568entanglement transmissionquantum communicationcomplex quantum networkentangled statepercolation |
| spellingShingle | Chuanxin Wang Xinqi Hu Gaogao Dong Exploring the Percolation Phenomena in Quantum Networks Mathematics entanglement transmission quantum communication complex quantum network entangled state percolation |
| title | Exploring the Percolation Phenomena in Quantum Networks |
| title_full | Exploring the Percolation Phenomena in Quantum Networks |
| title_fullStr | Exploring the Percolation Phenomena in Quantum Networks |
| title_full_unstemmed | Exploring the Percolation Phenomena in Quantum Networks |
| title_short | Exploring the Percolation Phenomena in Quantum Networks |
| title_sort | exploring the percolation phenomena in quantum networks |
| topic | entanglement transmission quantum communication complex quantum network entangled state percolation |
| url | https://www.mdpi.com/2227-7390/12/22/3568 |
| work_keys_str_mv | AT chuanxinwang exploringthepercolationphenomenainquantumnetworks AT xinqihu exploringthepercolationphenomenainquantumnetworks AT gaogaodong exploringthepercolationphenomenainquantumnetworks |