{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:44:27Z","timestamp":1760240667589,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,28]],"date-time":"2019-08-28T00:00:00Z","timestamp":1566950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010012","name":"National Aerospace Science Foundation of China","doi-asserted-by":"publisher","award":["11574081, 11374096 and 11074072"],"award-info":[{"award-number":["11574081, 11374096 and 11074072"]}],"id":[{"id":"10.13039\/501100010012","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of Hunan Province","doi-asserted-by":"publisher","award":["2017JJ2214"],"award-info":[{"award-number":["2017JJ2214"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Research Foundation of Education Department of Hunan Province","award":["17C1264"],"award-info":[{"award-number":["17C1264"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An efficient scheme is proposed in this study to prepare four symmetric hyperentangled cluster states in the polarization degrees of freedom (DOF) and spatial DOF with a two-photon system. This system consists of two nitrogen-vacancy (NV) centers which are coupled to two microtoroidal resonators. The two-photon polarization-spatial hyperentangled cluster states can be generated with our system by virtue of the input and output process. Compared with previous works, our quantum circuit for preparing the hyperentangled cluster states is simple and economic. Moreover, our scheme works deterministically and does not need any extra qubits, making it applicable to existing technologies. Our calculations show that our scheme has high fidelity with current technology, which can help hyperentangled cluster states to play a very useful role in quantum communication networks with long distances and high capacity.<\/jats:p>","DOI":"10.3390\/sym11091079","type":"journal-article","created":{"date-parts":[[2019,8,28]],"date-time":"2019-08-28T11:23:18Z","timestamp":1566991398000},"page":"1079","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["High-Fidelity Hyperentangled Cluster States of Two-Photon Systems and Their Applications"],"prefix":"10.3390","volume":"11","author":[{"given":"Liu","family":"Tan","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering and Photoelectric Physics, Hunan Engineering Laboratory for Preparation Technology of Polyvinyl Alcohol Fiber Material, Huaihua University, Huaihua 418008, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0817-8394","authenticated-orcid":false,"given":"Fang","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering and Photoelectric Physics, Hunan Engineering Laboratory for Preparation Technology of Polyvinyl Alcohol Fiber Material, Huaihua University, Huaihua 418008, China"},{"name":"Department of Basic Course, Hunan Police Academy, Changsha 410138, China"},{"name":"Synergetic Innovation Center for Quantum Effects and Application, Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, School of Physics and Electronics, Hunan Normal University, Changsha 410081, China"}]},{"given":"Lingxia","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering and Photoelectric Physics, Hunan Engineering Laboratory for Preparation Technology of Polyvinyl Alcohol Fiber Material, Huaihua University, Huaihua 418008, China"}]},{"given":"Shaohua","family":"Xiang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering and Photoelectric Physics, Hunan Engineering Laboratory for Preparation Technology of Polyvinyl Alcohol Fiber Material, Huaihua University, Huaihua 418008, China"}]},{"given":"Kehui","family":"Song","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering and Photoelectric Physics, Hunan Engineering Laboratory for Preparation Technology of Polyvinyl Alcohol Fiber Material, Huaihua University, Huaihua 418008, China"}]},{"given":"Yujing","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering and Photoelectric Physics, Hunan Engineering Laboratory for Preparation Technology of Polyvinyl Alcohol Fiber Material, Huaihua University, Huaihua 418008, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.physleta.2005.04.060","article-title":"Entanglement of the Hermite\u2013Gaussian modes states of photons","volume":"341","author":"Ren","year":"2005","journal-title":"Phys. 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