{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T16:01:56Z","timestamp":1776096116792,"version":"3.50.1"},"reference-count":53,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T00:00:00Z","timestamp":1651449600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Innovation Program of Shanghai Municipal Education Commission","award":["2021-01-07-00-08-E00100"],"award-info":[{"award-number":["2021-01-07-00-08-E00100"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11874155"],"award-info":[{"award-number":["11874155"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["91436211"],"award-info":[{"award-number":["91436211"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11374104"],"award-info":[{"award-number":["11374104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12174110"],"award-info":[{"award-number":["12174110"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Basic Research Project of Shanghai Science and Technology Com- mission","award":["20JC1416100"],"award-info":[{"award-number":["20JC1416100"]}]},{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai","doi-asserted-by":"crossref","award":["17ZR1442900"],"award-info":[{"award-number":["17ZR1442900"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Minhang Leading Talents","award":["201971"],"award-info":[{"award-number":["201971"]}]},{"name":"Shanghai Sailing Program","award":["21YF1410800"],"award-info":[{"award-number":["21YF1410800"]}]},{"name":"Shanghai Municipal Science and Technology Major Project","award":["2019SHZDZX01"],"award-info":[{"award-number":["2019SHZDZX01"]}]},{"name":"the 111 project","award":["B12024"],"award-info":[{"award-number":["B12024"]}]},{"name":"European Union\u2019s Horizon 2020 research and innovation programme","award":["899587"],"award-info":[{"award-number":["899587"]}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"crossref","award":["ANR-21-CE47-0005"],"award-info":[{"award-number":["ANR-21-CE47-0005"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Entanglement is an indispensable quantum resource for quantum information technology. In continuous-variable quantum optics, photon subtraction can increase the entanglement between Gaussian states of light, but for mixed states the extent of this entanglement increase is poorly understood. In this work, we use an entanglement measure based the R\u00e9nyi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log 2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon. The upper bound is valid for all Gaussian input states, regardless of the number of modes and the purity.<\/jats:p>","DOI":"10.22331\/q-2022-05-02-704","type":"journal-article","created":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T12:18:22Z","timestamp":1651493902000},"page":"704","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Maximal entanglement increase with single-photon subtraction"],"prefix":"10.22331","volume":"6","author":[{"given":"Kun","family":"Zhang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China"}]},{"given":"Jietai","family":"Jing","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China"},{"name":"CAS Center for Excellence in Ultra-intense Laser Science, Shanghai 201800, China"},{"name":"Department of Physics, Zhejiang University, Hangzhou 310027, China"},{"name":"Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China"}]},{"given":"Nicolas","family":"Treps","sequence":"additional","affiliation":[{"name":"Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, 4 place Jussieu, F-75252 Paris, France"}]},{"given":"Mattia","family":"Walschaers","sequence":"additional","affiliation":[{"name":"Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, 4 place Jussieu, F-75252 Paris, France"}]}],"member":"9598","published-online":{"date-parts":[[2022,5,2]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. A 47, 777 (1935).","DOI":"10.1103\/PhysRev.47.777"},{"key":"1","doi-asserted-by":"publisher","unstructured":"V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. Lett. 96, 010401 (2006).","DOI":"10.1103\/PhysRevLett.96.010401"},{"key":"2","doi-asserted-by":"publisher","unstructured":"C. H. Bennett, G. Brassard, C. Cr\u00e9peau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).","DOI":"10.1103\/PhysRevLett.70.1895"},{"key":"3","doi-asserted-by":"publisher","unstructured":"P. W. Shor, Phys. Rev. A 52, R2493 (1995).","DOI":"10.1103\/PhysRevA.52.R2493"},{"key":"4","doi-asserted-by":"publisher","unstructured":"S. Steinlechner, J. Bauchrowitz, M. Meinders, H. M\u00fcller-Ebhardt, K. Danzmann, R. Schnabel, Nat. Photon. 7, 626 (2013).","DOI":"10.1038\/nphoton.2013.150"},{"key":"5","doi-asserted-by":"publisher","unstructured":"B. Schumacher, and M. A. Nielsen, Phys. Rev. A 54, 2629 (1996).","DOI":"10.1103\/PhysRevA.54.2629"},{"key":"6","doi-asserted-by":"publisher","unstructured":"S. Lloyd, Phys. Rev. A 55, 1613 (1997).","DOI":"10.1103\/PhysRevA.55.1613"},{"key":"7","doi-asserted-by":"publisher","unstructured":"R. Raussendorf, and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).","DOI":"10.1103\/PhysRevLett.86.5188"},{"key":"8","doi-asserted-by":"publisher","unstructured":"E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).","DOI":"10.1038\/35051009"},{"key":"9","doi-asserted-by":"publisher","unstructured":"S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).","DOI":"10.1103\/RevModPhys.77.513"},{"key":"10","doi-asserted-by":"publisher","unstructured":"X. Su, Y. Zhao, S. Hao, X. Jia, C. Xie, and K. Peng, Opt. Lett. 37, 5178 (2012).","DOI":"10.1364\/OL.37.005178"},{"key":"11","doi-asserted-by":"publisher","unstructured":"S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, Nat. Commun. 3, 1206 (2012).","DOI":"10.1038\/ncomms2033"},{"key":"12","doi-asserted-by":"publisher","unstructured":"M. Chen, N. C. Menicucci, and O. Pfister, Phys. Rev. Lett. 112, 120505 (2014).","DOI":"10.1103\/PhysRevLett.112.120505"},{"key":"13","doi-asserted-by":"publisher","unstructured":"J. Roslund, R. M. de Ara\u00fajo, S. Jiang, C. Fabre, and N. Treps, Nat. Photon. 8, 109 (2014).","DOI":"10.1038\/nphoton.2013.340"},{"key":"14","doi-asserted-by":"publisher","unstructured":"S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, Phys. Rev. Lett. 114, 050501 (2015).","DOI":"10.1103\/PhysRevLett.114.050501"},{"key":"15","doi-asserted-by":"publisher","unstructured":"J.-i. Yoshikawa, S. Yokoyama, T. Kaji, C. Sornphiphatphong, Y. Shiozawa, K. Makino, and A. Furusawa, APL Photonics 1, 060801 (2016).","DOI":"10.1063\/1.4962732"},{"key":"16","doi-asserted-by":"publisher","unstructured":"K. Zhang, W. Wang, S. Liu, X. Pan, J. Du, Y. Lou, S. Yu, S. Lv, N. Treps, C. Fabre, and J. Jing, Phys. Rev. Lett. 124, 090501 (2020).","DOI":"10.1103\/PhysRevLett.124.090501"},{"key":"17","doi-asserted-by":"publisher","unstructured":"W. Wang, K. Zhang, and J. Jing, Phys. Rev. Lett. 125, 140501 (2020).","DOI":"10.1103\/PhysRevLett.125.140501"},{"key":"18","doi-asserted-by":"publisher","unstructured":"S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, Phys. Rev. Lett. 88, 097904 (2002).","DOI":"10.1103\/PhysRevLett.88.097904"},{"key":"19","doi-asserted-by":"publisher","unstructured":"A. Mari and J. Eisert, Phys. Rev. Lett. 109, 230503 (2012).","DOI":"10.1103\/PhysRevLett.109.230503"},{"key":"20","doi-asserted-by":"publisher","unstructured":"S. Rahimi-Keshari, T. C. Ralph, and C. M. Caves, Phys. Rev. X 6, 021039 (2016).","DOI":"10.1103\/PhysRevX.6.021039"},{"key":"21","doi-asserted-by":"publisher","unstructured":"A. Zavatta, V. Parigi, and M. Bellini, Phys. Rev. A 75, 052106 (2007).","DOI":"10.1103\/PhysRevA.75.052106"},{"key":"22","doi-asserted-by":"publisher","unstructured":"J. Wenger, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 92, 153601 (2004).","DOI":"10.1103\/PhysRevLett.92.153601"},{"key":"23","doi-asserted-by":"publisher","unstructured":"A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 98, 030502 (2007).","DOI":"10.1103\/PhysRevLett.98.030502"},{"key":"24","doi-asserted-by":"publisher","unstructured":"V. Parigi, A. Zavatta, M. Kim, and M. Bellini, Science 317, 1890 (2007).","DOI":"10.1126\/science.1146204"},{"key":"25","doi-asserted-by":"publisher","unstructured":"Y.-S. Ra, A. Dufour, M. Walschaers, C. Jacquard, T. Michel, C. Fabre, and N. Treps, Nat. Phys. 16, 144 - 147 (2020).","DOI":"10.1038\/s41567-019-0726-y"},{"key":"26","doi-asserted-by":"publisher","unstructured":"P. T. Cochrane, T. C. Ralph, and G. J. Milburn, Phys. Rev. A 65, 062306 (2002).","DOI":"10.1103\/PhysRevA.65.062306"},{"key":"27","doi-asserted-by":"publisher","unstructured":"S. Olivares, M. G. A. Paris, and R. Bonifacio, Phys. Rev. A 67, 032314 (2003).","DOI":"10.1103\/PhysRevA.67.032314"},{"key":"28","doi-asserted-by":"publisher","unstructured":"Y. Yang, and F.-L. Li, Phys. Rev. A 80, 022315 (2009).","DOI":"10.1103\/PhysRevA.80.022315"},{"key":"29","doi-asserted-by":"publisher","unstructured":"C. Navarrete-Benlloch, R. Garc\u00eda-Patr\u00f3n, J. H. Shapiro, and N. J. Cerf, Phys. Rev. A 86, 012328 (2012).","DOI":"10.1103\/PhysRevA.86.012328"},{"key":"30","doi-asserted-by":"publisher","unstructured":"M. Walschaers, C. Fabre, V. Parigi, and N. Treps, Phys. Rev. Lett. 119, 183601 (2017).","DOI":"10.1103\/PhysRevLett.119.183601"},{"key":"31","doi-asserted-by":"publisher","unstructured":"M. Walschaers, C. Fabre, V. Parigi, and N. Treps, Phys. Rev. A. 96, 053835 (2017).","DOI":"10.1103\/PhysRevA.96.053835"},{"key":"32","doi-asserted-by":"publisher","unstructured":"M. Walschaers, S. Sarkar, V. Parigi, and N. Treps, Phys. Rev. Lett. 121, 220501 (2018).","DOI":"10.1103\/PhysRevLett.121.220501"},{"key":"33","doi-asserted-by":"publisher","unstructured":"J. Eisert, S. Scheel, and M. B. Plenio, Phys. Rev. Lett. 89, 137903 (2002).","DOI":"10.1103\/PhysRevLett.89.137903"},{"key":"34","doi-asserted-by":"publisher","unstructured":"J. Fiur\u00e1\u0161ek, Phys. Rev. Lett. 89, 137904 (2002).","DOI":"10.1103\/PhysRevLett.89.137904"},{"key":"35","doi-asserted-by":"publisher","unstructured":"G. Giedke, and J. I. Cirac Phys. Rev. A 66, 032316 (2002).","DOI":"10.1103\/PhysRevA.66.032316"},{"key":"36","doi-asserted-by":"publisher","unstructured":"H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki Nat. Photon. 4, 178\u2013181 (2010).","DOI":"10.1038\/nphoton.2010.1"},{"key":"37","doi-asserted-by":"publisher","unstructured":"G. Vidal, and R. F. Werner, Phys. Rev. A 65, 032314 (2002).","DOI":"10.1103\/PhysRevA.65.032314"},{"key":"38","doi-asserted-by":"publisher","unstructured":"R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).","DOI":"10.1103\/RevModPhys.81.865"},{"key":"39","doi-asserted-by":"publisher","unstructured":"C. H. Bennett, D. P. DiVincenzo, R. F.Werner, and W. K.Wootters, Phys. Rev. A 54, 3824 (1996).","DOI":"10.1103\/PhysRevA.54.3824"},{"key":"40","doi-asserted-by":"publisher","unstructured":"G. T\u00f3th, T. Moroder, and O. G\u00fchne, Phys. Rev. Lett. 114, 160501 (2015).","DOI":"10.1103\/PhysRevLett.114.160501"},{"key":"41","doi-asserted-by":"publisher","unstructured":"J. S. Kim, and B. C. Sanders, J. Phys. A: Math. Theor. 43, 445305 (2010).","DOI":"10.1088\/1751-8113\/43\/44\/445305"},{"key":"42","doi-asserted-by":"publisher","unstructured":"G. Adesso, and A. Serafini, Phys. Rev. Lett. 109, 190502 (2012).","DOI":"10.1103\/PhysRevLett.109.190502"},{"key":"43","doi-asserted-by":"publisher","unstructured":"L. Lami, C. Hirche, G. Adesso, and A. Winter, Phys. Rev. Lett. 117, 220502 (2016).","DOI":"10.1103\/PhysRevLett.117.220502"},{"key":"44","doi-asserted-by":"publisher","unstructured":"L. Lami, L. Mi\u0161ta, Jr., and G. Adesso, ArXiv 2010.15729 (2020).","DOI":"10.48550\/arXiv.2010.15729"},{"key":"45","doi-asserted-by":"publisher","unstructured":"C. Fabre and N. Treps, Rev. Mod. Phys. 92 035005 (2020).","DOI":"10.1103\/RevModPhys.92.035005"},{"key":"46","doi-asserted-by":"publisher","unstructured":"M. Walschaers, PRX Quantum 2 030204 (2021).","DOI":"10.1103\/PRXQuantum.2.030204"},{"key":"47","doi-asserted-by":"publisher","unstructured":"C. Weedbrook, S. Pirandola, R. Garc\u00eda-Patr\u00f3n, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Ralph, Rev. Mod. Phys 84, 621 (2012).","DOI":"10.1103\/RevModPhys.84.621"},{"key":"48","doi-asserted-by":"publisher","unstructured":"M. M.Wolf, G. Giedke, O. Kr\u00fcger, R. F.Werner, and J. I. Cirac, Phys. Rev. A 69, 052320 (2004).","DOI":"10.1103\/PhysRevA.69.052320"},{"key":"49","doi-asserted-by":"publisher","unstructured":"C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).","DOI":"10.1103\/PhysRevA.53.2046"},{"key":"50","doi-asserted-by":"publisher","unstructured":"M. Walschaers, Y.-S. Ra, and N. Treps, Phys. Rev. A 100, 023828 (2019).","DOI":"10.1103\/PhysRevA.100.023828"},{"key":"51","doi-asserted-by":"publisher","unstructured":"M. Walschaers, and N. Treps, Phys. Rev. Lett. 124, 150501 (2020).","DOI":"10.1103\/PhysRevLett.124.150501"},{"key":"52","doi-asserted-by":"publisher","unstructured":"M. Walschaers, V. Parigi, N. Treps, PRX Quantum 1, 020305 (2020).","DOI":"10.1103\/PRXQuantum.1.020305"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-05-02-704\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T12:18:43Z","timestamp":1651493923000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-05-02-704\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,2]]},"references-count":53,"URL":"https:\/\/doi.org\/10.22331\/q-2022-05-02-704","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,2]]},"article-number":"704"}}