{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:27:12Z","timestamp":1740137232059,"version":"3.37.3"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,3,9]],"date-time":"2019-03-09T00:00:00Z","timestamp":1552089600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671082"],"award-info":[{"award-number":["61671082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1007\/s11128-019-2238-1","type":"journal-article","created":{"date-parts":[[2019,3,9]],"date-time":"2019-03-09T07:02:42Z","timestamp":1552114962000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The critical detection efficiency for closing the detection loophole of some modified Bell inequalities"],"prefix":"10.1007","volume":"18","author":[{"given":"Dan-Dan","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya","family":"Cao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiao-Yan","family":"Wen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,3,9]]},"reference":[{"issue":"10","key":"2238_CR1","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1103\/PhysRev.47.777","volume":"47","author":"A Einstein","year":"1935","unstructured":"Einstein, A., Podolsky, B., Rosen, N.: Can quantummechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777 (1935)","journal-title":"Phys. Rev."},{"key":"2238_CR2","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1103\/PhysicsPhysiqueFizika.1.195","volume":"1","author":"J Bell","year":"1964","unstructured":"Bell, J.: On the Einstein\u2013Podolsy\u2013Rosen paradox. Physics 1, 195 (1964)","journal-title":"Physics"},{"key":"2238_CR3","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1103\/RevModPhys.86.419","volume":"86","author":"N Brunner","year":"2014","unstructured":"Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)","journal-title":"Rev. Mod. Phys."},{"key":"2238_CR4","doi-asserted-by":"publisher","first-page":"250401","DOI":"10.1103\/PhysRevLett.115.250401","volume":"115","author":"M Giustina","year":"2015","unstructured":"Giustina, M., Versteegh, M.A.M., Wengerowsky, S., et al.: Significant-loophole-free test of Bell\u2019s theorem with entangled photons. Phys. Rev. Lett. 115, 250401 (2015)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR5","doi-asserted-by":"publisher","first-page":"010402","DOI":"10.1103\/PhysRevLett.119.010402","volume":"119","author":"W Rosenfeld","year":"2017","unstructured":"Rosenfeld, W., Burchardt, D., Garthoff, R., et al.: Event-ready bell test using entangled atoms simultaneously closing detection and locality loopholes. Phys. Rev. Lett. 119, 010402 (2017)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR6","doi-asserted-by":"publisher","first-page":"3831","DOI":"10.1103\/PhysRevD.35.3831","volume":"35","author":"A Garg","year":"1987","unstructured":"Garg, A., Mermin, N.D.: Detector inefficiencies in the Einstein\u2013Podolsky\u2013Rosen experiment. Phys. Rev. D 35, 3831 (1987)","journal-title":"Phys. Rev. D"},{"key":"2238_CR7","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1103\/PhysRevA.47.R747","volume":"47","author":"PH Eberhard","year":"1993","unstructured":"Eberhard, P.H.: Background level and counter efficiencies required for a loophole free Einstein\u2013Podolsky\u2013Rosen experiment. Phys. Rev. A 47, 747\u2013750 (1993)","journal-title":"Phys. Rev. A"},{"key":"2238_CR8","doi-asserted-by":"publisher","first-page":"230501","DOI":"10.1103\/PhysRevLett.98.230501","volume":"98","author":"A Ac\u00edn","year":"2007","unstructured":"Ac\u00edn, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., Scarani, V.: Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR9","doi-asserted-by":"publisher","first-page":"062327","DOI":"10.1103\/PhysRevA.80.062327","volume":"80","author":"CE Bardyn","year":"2009","unstructured":"Bardyn, C.E., Liew, T.C., Massar, S., Mckague, M., Scarani, V.: Device-independent state estimation based on Bell\u2019s inequalities. Phys. Rev. A 80, 062327 (2009)","journal-title":"Phys. Rev. A"},{"key":"2238_CR10","doi-asserted-by":"publisher","first-page":"120405","DOI":"10.1103\/PhysRevLett.97.120405","volume":"97","author":"A Ac\u00edn","year":"2006","unstructured":"Ac\u00edn, A., Gisin, N., Masanes, L.: From Bell\u2019s theorem to secure quantum key distribution. Phys. Rev. Lett. 97, 120405 (2006)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR11","doi-asserted-by":"publisher","first-page":"140501","DOI":"10.1103\/PhysRevLett.113.140501","volume":"113","author":"U Vazirani","year":"2014","unstructured":"Vazirani, U., Vidick, T.: Fully device-independent quantum key distribution. Phys. Rev. Lett. 113, 140501 (2014)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR12","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1038\/nature09008","volume":"464","author":"S Pironio","year":"2010","unstructured":"Pironio, S., Ac\u00edn, A., Massar, S., de La Giroday, A.B., Matsukevich, D.N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T.A., Monroe, C.: Random numbers certified by Bell\u2019s theorem. Nature 464, 1021 (2010)","journal-title":"Nature"},{"key":"2238_CR13","doi-asserted-by":"publisher","first-page":"012336","DOI":"10.1103\/PhysRevA.87.012336","volume":"87","author":"S Pironio","year":"2013","unstructured":"Pironio, S., Massar, S.: Security of practical private randomness generation. Phys. Rev. A 87, 012336 (2013)","journal-title":"Phys. Rev. A"},{"key":"2238_CR14","doi-asserted-by":"publisher","first-page":"012335","DOI":"10.1103\/PhysRevA.87.012335","volume":"87","author":"S Fehr","year":"2013","unstructured":"Fehr, S., Gelles, R., Schaffner, C.: Security and composability of randomness expansion from Bell inequalities. Phys. Rev. A 87, 012335 (2013)","journal-title":"Phys. Rev. A"},{"key":"2238_CR15","doi-asserted-by":"publisher","first-page":"032319","DOI":"10.1103\/PhysRevA.88.032319","volume":"88","author":"P Mironowicz","year":"2013","unstructured":"Mironowicz, P., Paw\u0142owski, M.: Robustness of quantum-randomness expansion protocols in the presence of noise. Phys. Rev. A 88, 032319 (2013)","journal-title":"Phys. Rev. A"},{"key":"2238_CR16","doi-asserted-by":"publisher","first-page":"16200","DOI":"10.1038\/srep16200","volume":"5","author":"H-W Li","year":"2015","unstructured":"Li, H.-W., Yin, Z.Q., Wang, S., Qian, Y.J., Chen, W., Guo, G.C., Han, Z.F.: Randomness determines practical security of BB84 quantum key distribution. Sci. Rep. 5, 16200 (2015)","journal-title":"Sci. Rep."},{"key":"2238_CR17","doi-asserted-by":"publisher","first-page":"15543","DOI":"10.1038\/srep15543","volume":"5","author":"D-D Li","year":"2015","unstructured":"Li, D.-D., Wen, Q.Y., Wang, Y.K., Zhou, Y.Q., Gao, F.: Security of semi-device-independent random number expansion protocols. Sci. Rep. 5, 15543 (2015)","journal-title":"Sci. Rep."},{"key":"2238_CR18","doi-asserted-by":"publisher","first-page":"012104","DOI":"10.1103\/PhysRevA.94.012104","volume":"94","author":"D-D Li","year":"2016","unstructured":"Li, D.-D., Zhou, Y.Q., Gao, F., Li, X.H., Wen, Q.Y.: Effects of measurement dependence on generalized Clauser\u2013Horne\u2013Shimony\u2013Holt Bell test in the single-run and multiple-run scenarios. Phys. Rev. A 94, 012104 (2016)","journal-title":"Phys. Rev. A"},{"key":"2238_CR19","doi-asserted-by":"publisher","first-page":"052308","DOI":"10.1103\/PhysRevA.85.052308","volume":"85","author":"H-W Li","year":"2012","unstructured":"Li, H.-W., Paw\u0142owski, M., Yin, Z.Q., Guo, G.C., Han, Z.F.: Semi-device-independent randomness certification using \n                    \n                      \n                    \n                    $$n\\rightarrow 1$$\n                    \n                      \n                        \n                          n\n                          \u2192\n                          1\n                        \n                      \n                    \n                   quantum random access codes. Phys. Rev. A 85, 052308 (2012)","journal-title":"Phys. Rev. A"},{"key":"2238_CR20","doi-asserted-by":"publisher","first-page":"022301","DOI":"10.1103\/PhysRevA.83.022301","volume":"83","author":"M Jakobi","year":"2011","unstructured":"Jakobi, M., Simon, C., Gisin, N., Bancal, J.D., Branciard, C., Walenta, N.: Practical private database queries based on a quantum-key-distribution protocol. Phys. Rev. A 83, 022301 (2011)","journal-title":"Phys. Rev. A"},{"key":"2238_CR21","first-page":"6600111","volume":"21","author":"F Gao","year":"2015","unstructured":"Gao, F., Liu, B., Huang, W., Wen, Q.Y.: Postprocessing of the oblivious key in quantum private query. IEEE. J. Sel. Top. Quant. 21, 6600111 (2015)","journal-title":"IEEE. J. Sel. Top. Quant."},{"key":"2238_CR22","doi-asserted-by":"publisher","first-page":"042318","DOI":"10.1103\/PhysRevA.93.042318","volume":"93","author":"CY Wei","year":"2016","unstructured":"Wei, C.Y., Wang, T.Y., Gao, F.: Practical quantum private query with better performance in resisting joint-measurement attack. Phys. Rev. A 93, 042318 (2016)","journal-title":"Phys. Rev. A"},{"key":"2238_CR23","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1109\/TC.2017.2721404","volume":"99","author":"CY Wei","year":"2018","unstructured":"Wei, C.Y., Cai, X.Q., Liu, B., Wang, T.Y., Gao, F.: A generic construction of quantum-oblivious-key-transfer-based private query with ideal database security and zero failure. IEEE Trans. Comput. 99, 2\u20138 (2018)","journal-title":"IEEE Trans. Comput."},{"key":"2238_CR24","doi-asserted-by":"publisher","first-page":"100301","DOI":"10.1007\/s11433-015-5714-3","volume":"58","author":"B Liu","year":"2015","unstructured":"Liu, B., Gao, F., Wei, C., Wen, Q.Y.: Qkd-based quantum private query without a failure probability. Sci. China Phys. Mech. Astron. 58, 100301 (2015)","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"2238_CR25","doi-asserted-by":"publisher","first-page":"791","DOI":"10.1038\/35057215","volume":"409","author":"MA Rowe","year":"2001","unstructured":"Rowe, M.A., et al.: Experimental violation of a Bell\u2019s inequality with efficient detection. Nature 409, 791\u2013794 (2001)","journal-title":"Nature"},{"key":"2238_CR26","doi-asserted-by":"publisher","first-page":"150404","DOI":"10.1103\/PhysRevLett.100.150404","volume":"100","author":"DN Matsukevich","year":"2008","unstructured":"Matsukevich, D.N., Maunz, P., Moehring, D.L., Olmschenk, S., Monroe, C.: Bell inequality violation with two remote atomic qubits. Phys. Rev. Lett. 100, 150404 (2008)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR27","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1038\/nature08363","volume":"461","author":"M Ansmann","year":"2009","unstructured":"Ansmann, M., et al.: Violation of Bell\u2019s inequality in Josephson phase qubits. Nature 461, 504\u2013506 (2009)","journal-title":"Nature"},{"key":"2238_CR28","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1126\/science.1221856","volume":"337","author":"J Hofmann","year":"2012","unstructured":"Hofmann, J., et al.: Heralded entanglement between widely separated atoms. Science 337, 72\u201375 (2012)","journal-title":"Science"},{"key":"2238_CR29","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1038\/nature12012","volume":"497","author":"M Giustina","year":"2013","unstructured":"Giustina, M., et al.: Bell violation using entangled photons without the fair-sampling assumption. Nature 497, 227\u2013230 (2013)","journal-title":"Nature"},{"key":"2238_CR30","doi-asserted-by":"publisher","first-page":"130406","DOI":"10.1103\/PhysRevLett.111.130406","volume":"111","author":"BG Christensen","year":"2013","unstructured":"Christensen, B.G., McCusker, K.T., Altepeter, J.B., et al.: Detection-loophole-free test of quantum nonlocality, and applications. Phys. Rev. Lett. 111, 130406 (2013)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR31","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1038\/nature15759","volume":"526","author":"B Hensen","year":"2015","unstructured":"Hensen, B., Bernien, H., Dr\u00e9au, A.E., et al.: Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682 (2015)","journal-title":"Nature"},{"key":"2238_CR32","doi-asserted-by":"publisher","first-page":"3304","DOI":"10.1103\/PhysRevA.57.3304","volume":"57","author":"J-\u00c5 Larsson","year":"1998","unstructured":"Larsson, J.-\u00c5.: Bell\u2019s inequality and detector inefficiency. Phys. Rev. A 57, 3304 (1998)","journal-title":"Phys. Rev. A"},{"key":"2238_CR33","doi-asserted-by":"publisher","first-page":"062109","DOI":"10.1103\/PhysRevA.79.062109","volume":"79","author":"A Cabello","year":"2009","unstructured":"Cabello, A., Larsson, J.-\u00c5., Rodr\u00edguez, D.: Minimum detection efficiency required for a loophole-free violation of the Braunstein\u2013Caves chained Bell inequalities. Phys. Rev. A 79, 062109 (2009)","journal-title":"Phys. Rev. A"},{"key":"2238_CR34","doi-asserted-by":"publisher","first-page":"010401","DOI":"10.1103\/PhysRevLett.116.010401","volume":"116","author":"G P\u00fctz","year":"2016","unstructured":"P\u00fctz, G., Martin, A., Gisin, N., Aktas, D., Fedrici, B., Tanzilli, S.: Quantum nonlocality with arbitrary limited detection efficiency. Phys. Rev. Lett. 116, 010401 (2016)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR35","doi-asserted-by":"publisher","first-page":"034102","DOI":"10.1103\/PhysRevA.86.034102","volume":"86","author":"Y Xiang","year":"2012","unstructured":"Xiang, Y., Wang, H.-X., Hong, F.-Y.: Detection efficiency in the loophole-free violation of Svetlichny\u2019s inequality. Phys. Rev. A 86, 034102 (2012)","journal-title":"Phys. Rev. A"},{"key":"2238_CR36","doi-asserted-by":"publisher","first-page":"120402","DOI":"10.1103\/PhysRevLett.101.120402","volume":"101","author":"A Cabello","year":"2008","unstructured":"Cabello, A., Rodr\u00edguez, D., Villanueva, I.: Necessary and sufficient detection efficiency for the Mermin inequalities. Phys. Rev. Lett. 101, 120402 (2008)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR37","doi-asserted-by":"publisher","first-page":"012113","DOI":"10.1103\/PhysRevA.87.012113","volume":"87","author":"G Ca\u00f1as","year":"2013","unstructured":"Ca\u00f1as, G., Barra, J.F., G\u00f3mez, E.S., Lima, G., Sciarrino, F., Cabello, A.: Detection efficiency for loophole-free Bell tests with entangled states affected by colored noise. Phys. Rev. A 87, 012113 (2013)","journal-title":"Phys. Rev. A"},{"key":"2238_CR38","doi-asserted-by":"publisher","first-page":"062109","DOI":"10.1103\/PhysRevA.68.062109","volume":"68","author":"S Massar","year":"2003","unstructured":"Massar, S., Pironio, S.: Violation of local realism versus detection efficiency. Phys. Rev. A 68, 062109 (2003)","journal-title":"Phys. Rev. A"},{"key":"2238_CR39","doi-asserted-by":"publisher","first-page":"022117","DOI":"10.1103\/PhysRevA.63.022117","volume":"63","author":"J-\u00c5 Larsson","year":"2001","unstructured":"Larsson, J.-\u00c5., Semitecolos, J.: Strict detector-efficiency bounds for n-site Clauser\u2013Horne inequalities. Phys. Rev. A 63, 022117 (2001)","journal-title":"Phys. Rev. A"},{"key":"2238_CR40","doi-asserted-by":"publisher","first-page":"060401","DOI":"10.1103\/PhysRevLett.104.060401","volume":"104","author":"T V\u00e9rtesi","year":"2010","unstructured":"V\u00e9rtesi, T., Pironio, S., Brunner, N.: Closing the detection loophole in Bell experiments using qudits. Phys. Rev. Lett. 104, 060401 (2010)","journal-title":"Phys. Rev. Lett."},{"key":"2238_CR41","doi-asserted-by":"publisher","first-page":"032121","DOI":"10.1103\/PhysRevA.65.032121","volume":"65","author":"S Massar","year":"2002","unstructured":"Massar, S.: Nonlocality, closing the detection loophole, and communication complexity. Phys. Rev. A 65, 032121 (2002)","journal-title":"Phys. Rev. A"},{"key":"2238_CR42","doi-asserted-by":"publisher","first-page":"022103","DOI":"10.1103\/PhysRevA.92.022103","volume":"92","author":"KF P\u00e1l","year":"2015","unstructured":"P\u00e1l, K.F., V\u00e9rtesi, T.: Closing the detection loophole in tripartite Bell tests using the W state. Phys. Rev. A 92, 022103 (2015)","journal-title":"Phys. Rev. A"},{"key":"2238_CR43","doi-asserted-by":"publisher","first-page":"052104","DOI":"10.1103\/PhysRevA.92.052104","volume":"92","author":"KF P\u00e1l","year":"2015","unstructured":"P\u00e1l, K.F., V\u00e9rtesi, T.: Bell inequalities violated using detectors of low efficiency. Phys. Rev. A 92, 052104 (2015)","journal-title":"Phys. Rev. A"},{"key":"2238_CR44","doi-asserted-by":"publisher","first-page":"062111","DOI":"10.1103\/PhysRevA.86.062111","volume":"86","author":"KF P\u00e1l","year":"2012","unstructured":"P\u00e1l, K.F., V\u00e9rtesi, T., Brunner, N.: Closing the detection loophole in multipartite Bell tests using Greenberger\u2013Horne\u2013Zeilinger states. Phys. Rev. A 86, 062111 (2012)","journal-title":"Phys. Rev. A"},{"key":"2238_CR45","doi-asserted-by":"publisher","first-page":"042126","DOI":"10.1103\/PhysRevA.94.042126","volume":"94","author":"Z Cao","year":"2016","unstructured":"Cao, Z., Peng, T.: Tight detection efficiency bounds of Bell tests in no-signaling theories. Phys. Rev. A. 94, 042126 (2016)","journal-title":"Phys. Rev. A."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2238-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-019-2238-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2238-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,8]],"date-time":"2020-03-08T00:23:25Z","timestamp":1583627005000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-019-2238-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,9]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["2238"],"URL":"https:\/\/doi.org\/10.1007\/s11128-019-2238-1","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"type":"print","value":"1570-0755"},{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2019,3,9]]},"assertion":[{"value":"5 September 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"123"}}