{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T14:19:58Z","timestamp":1765808398432,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,11,25]],"date-time":"2024-11-25T00:00:00Z","timestamp":1732492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62071064","2019XDA02","IPOC2022ZT10"],"award-info":[{"award-number":["62071064","2019XDA02","IPOC2022ZT10"]}]},{"name":"Fundamental Research Funds for the Central Universities of China","award":["62071064","2019XDA02","IPOC2022ZT10"],"award-info":[{"award-number":["62071064","2019XDA02","IPOC2022ZT10"]}]},{"name":"Fund of State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications","award":["62071064","2019XDA02","IPOC2022ZT10"],"award-info":[{"award-number":["62071064","2019XDA02","IPOC2022ZT10"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Controlled quantum teleportation is an important extension of multipartite quantum teleportation, which plays an indispensable role in building quantum networks. Compared with discrete variable counterparts, continuous variable controlled quantum teleportation can generate entanglement deterministically and exhibit higher superiority of the supervisor\u2019s authority. Here, we define a measure to quantify the control power in continuous variable controlled quantum teleportation via Greenberger\u2013Horne\u2013Zeilinger-type entangled coherent state channels. Our results show that control power in continuous variable controlled quantum teleportation increases with the mean photon number of coherent states. Its upper bound is 1\/2, which exceeds the upper bound in discrete variable controlled quantum teleportation (1\/3). The robustness of the protocol is analyzed with photon absorption. The results show that the improving ability of the control power will descend by the increasing photon loss, with the upper bound unchanged and robust. Our results illuminate the role of control power in multipartite continuous variable quantum information processing and provide a criterion for evaluating the quality of quantum communication networks.<\/jats:p>","DOI":"10.3390\/e26121017","type":"journal-article","created":{"date-parts":[[2024,11,25]],"date-time":"2024-11-25T05:21:32Z","timestamp":1732512092000},"page":"1017","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Control Power in Continuous Variable Controlled Quantum Teleportation"],"prefix":"10.3390","volume":"26","author":[{"given":"Yuehan","family":"Tian","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China"},{"name":"School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dunbo","family":"Cai","sequence":"additional","affiliation":[{"name":"China Mobile (Suzhou) Software Technology Company Limited, Suzhou 215163, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nengfei","family":"Gong","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China"},{"name":"School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yining","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China"},{"name":"School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling","family":"Qian","sequence":"additional","affiliation":[{"name":"China Mobile (Suzhou) Software Technology Company Limited, Suzhou 215163, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Runqing","family":"Zhang","sequence":"additional","affiliation":[{"name":"China Mobile (Suzhou) Software Technology Company Limited, Suzhou 215163, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiguo","family":"Huang","sequence":"additional","affiliation":[{"name":"China Mobile (Suzhou) Software Technology Company Limited, Suzhou 215163, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiejun","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China"},{"name":"School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1103\/PhysRevLett.70.1895","article-title":"Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels","volume":"70","author":"Bennett","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1038\/s42254-023-00588-x","article-title":"Progress in quantum teleportation","volume":"5","author":"Hu","year":"2023","journal-title":"Nat. Rev. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"230311","DOI":"10.1007\/s11433-023-2286-8","article-title":"Demonstration of controlled high-dimensional quantum teleportation","volume":"67","author":"Lv","year":"2024","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"010301","DOI":"10.7498\/aps.73.20231795","article-title":"Quantum information technology: Current status and prospects","volume":"73","author":"Pan","year":"2024","journal-title":"Acta Phys. Sin."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"040601","DOI":"10.1103\/PhysRevLett.132.040601","article-title":"Orbital angular momentum multiplexed deterministic all-optical quantum erasure-correcting code","volume":"132","author":"Lou","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1473","DOI":"10.1103\/PhysRevA.49.1473","article-title":"Teleportation of quantum states","volume":"49","author":"Vaidman","year":"1994","journal-title":"Phys. Rev. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1103\/RevModPhys.77.513","article-title":"Quantum information with continuous variables","volume":"77","author":"Braunstein","year":"2005","journal-title":"Rev. Mod. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2007.04.005","article-title":"Quantum information with Gaussian states","volume":"448","author":"Wang","year":"2007","journal-title":"Phys. Rep."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1103\/RevModPhys.84.621","article-title":"Gaussian quantum information","volume":"84","author":"Weedbrook","year":"2012","journal-title":"Rev. Mod. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"100801","DOI":"10.1103\/PhysRevLett.132.100801","article-title":"Deterministic all-optical quantum teleportation of four degrees of freedom","volume":"132","author":"Liu","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"230501","DOI":"10.1103\/PhysRevLett.118.230501","article-title":"Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states","volume":"118","author":"Deng","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"170403","DOI":"10.1103\/PhysRevLett.121.170403","article-title":"Demonstration of Einstein-Podolsky-Rosen steering using hybrid continuous-and discrete-variable entanglement of light","volume":"121","author":"Raskop","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1038\/nphys3410","article-title":"Hybrid discrete-and continuous-variable quantum information","volume":"11","author":"Andersen","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wen, J., Novikova, I., Qian, C., Zhang, C., and Du, S. (2021). Hybrid entanglement between optical discrete polarizations and continuous quadrature variables. Photonics, 8.","DOI":"10.3390\/photonics8120552"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"23284","DOI":"10.1109\/ACCESS.2022.3154468","article-title":"Hybrid CV-DV quantum communications and quantum networks","volume":"10","author":"Djordjevic","year":"2022","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"032434","DOI":"10.1103\/PhysRevA.105.032434","article-title":"Quantum teleportation of hybrid qubits and single-photon qubits using Gaussian resources","volume":"105","author":"Bose","year":"2022","journal-title":"Phys. Rev. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"033705","DOI":"10.1103\/PhysRevA.109.033705","article-title":"Implementing a cross-Kerr interaction between microwave and optical cavities and its application in generating a hybrid continuous-variable\u2013discrete-variable entangled state","volume":"109","author":"Xu","year":"2024","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"032406","DOI":"10.1103\/PhysRevA.109.032406","article-title":"Controlled state reconstruction and quantum secret sharing","volume":"109","author":"Singh","year":"2024","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"026006","DOI":"10.1117\/1.AP.5.2.026006","article-title":"Deterministic all-optical quantum state sharing","volume":"5","author":"Chen","year":"2023","journal-title":"Adv. Photonics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4394","DOI":"10.1103\/PhysRevA.58.4394","article-title":"Quantum teleportation using three-particle entanglement","volume":"58","author":"Karlsson","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"022338","DOI":"10.1103\/PhysRevA.72.022338","article-title":"Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement","volume":"72","author":"Deng","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"012323","DOI":"10.1103\/PhysRevA.101.012323","article-title":"Control power of high-dimensional controlled teleportation","volume":"101","author":"Wang","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"052433","DOI":"10.1103\/PhysRevA.106.052433","article-title":"Controlled quantum teleportation in the presence of an adversary","volume":"106","author":"Gangopadhyay","year":"2022","journal-title":"Phys. Rev. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"052339","DOI":"10.1103\/PhysRevA.101.052339","article-title":"Device-independent secret sharing and a stronger form of Bell nonlocality","volume":"101","author":"Moreno","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"150401","DOI":"10.1103\/PhysRevLett.129.150401","article-title":"Test of genuine multipartite nonlocality","volume":"129","author":"Mao","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"014102","DOI":"10.1103\/PhysRevA.88.014102","article-title":"Definitions of multipartite nonlocality","volume":"88","author":"Bancal","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1038\/nature02858","article-title":"Demonstration of a quantum teleportation network for continuous variables","volume":"431","author":"Yonezawa","year":"2004","journal-title":"Nature"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"170501","DOI":"10.1103\/PhysRevLett.122.170501","article-title":"Demonstration of controlled quantum teleportation for discrete variables on linear optical devices","volume":"122","author":"Lemr","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"052601","DOI":"10.1103\/PhysRevA.103.052601","article-title":"Control power of a high-dimensional controlled nonlocal quantum computation","volume":"103","author":"Gong","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"012306","DOI":"10.1103\/PhysRevA.99.012306","article-title":"Controlled teleportation of qubit states: Relation between teleportation faithfulness, controller\u2019s authority, and tripartite entanglement","volume":"99","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"032328","DOI":"10.1103\/PhysRevA.93.032328","article-title":"Minimal control power of the controlled teleportation","volume":"93","author":"Jeong","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"022313","DOI":"10.1103\/PhysRevA.64.022313","article-title":"Entangled coherent states: Teleportation and decoherence","volume":"64","author":"Hirota","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"022302","DOI":"10.1103\/PhysRevA.64.022302","article-title":"Quantum teleportation of entangled coherent states","volume":"64","author":"Wang","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"022321","DOI":"10.1103\/PhysRevA.68.022321","article-title":"Teleportation of coherent-state superpositions within a network","volume":"68","author":"An","year":"2003","journal-title":"Phys. Rev. A"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"044305","DOI":"10.1103\/PhysRevA.75.044305","article-title":"Improving the teleportation of entangled coherent states","volume":"75","author":"Prakash","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1852","DOI":"10.1007\/s10773-011-0700-7","article-title":"Controlled teleportation of an ECS by using a four-mode CTECS","volume":"50","author":"Liu","year":"2011","journal-title":"Int. J. Theor. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1007\/s10773-019-04014-w","article-title":"Controlled entanglement diversion using GHZ type entangled coherent state","volume":"58","author":"Prakash","year":"2019","journal-title":"Int. J. Theor. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1007\/s10773-022-05080-3","article-title":"Controlled bidirectional quantum teleportation of superposed coherent state using five-mode cluster-type entangled coherent state as a resource","volume":"61","author":"Pandey","year":"2022","journal-title":"Int. J. Theor. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"5529","DOI":"10.1364\/OL.443099","article-title":"Long-distance twin-field quantum key distribution with entangled sources","volume":"46","author":"Li","year":"2021","journal-title":"Opt. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Yin, H.L., and Chen, Z.B. (2019). Coherent-state-based twin-field quantum key distribution. Sci. Rep., 9.","DOI":"10.1038\/s41598-019-50429-0"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3342","DOI":"10.1007\/s10773-019-04207-3","article-title":"Controlled quantum teleportation of superposed coherent state using GHZ entangled coherent state","volume":"58","author":"Pandey","year":"2019","journal-title":"Int. J. Theor. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/0031-8914(74)90215-8","article-title":"Even and odd coherent states and excitations of a singular oscillator","volume":"72","author":"Dodonov","year":"1974","journal-title":"Physica"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"030503","DOI":"10.1103\/PhysRevLett.100.030503","article-title":"Fault-tolerant linear optical quantum computing with small-amplitude coherent states","volume":"100","author":"Lund","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"022104","DOI":"10.1103\/PhysRevA.74.022104","article-title":"Greenberger-Horne-Zeilinger\u2013type and W-type entangled coherent states: Generation and Bell-type inequality tests without photon counting","volume":"74","author":"Jeong","year":"2006","journal-title":"Phys. Rev. A"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Deng, X., Tian, C., Su, X., and Xie, C. (2017). Avoiding disentanglement of multipartite entangled optical beams with a correlated noisy channel. Sci. Rep., 7.","DOI":"10.1038\/srep44475"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"022308","DOI":"10.1103\/PhysRevA.72.022308","article-title":"Decoherence of multidimensional entangled coherent states","volume":"72","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1088\/0953-4075\/40\/8\/012","article-title":"Effect of decoherence on fidelity in teleportation using entangled coherent states","volume":"40","author":"Prakash","year":"2007","journal-title":"J. Phys. B At. Mol. Opt. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/12\/1017\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:38:52Z","timestamp":1760114332000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/12\/1017"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,25]]},"references-count":47,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["e26121017"],"URL":"https:\/\/doi.org\/10.3390\/e26121017","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2024,11,25]]}}}