{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T00:29:40Z","timestamp":1772756980111,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T00:00:00Z","timestamp":1581984000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["Pathos"],"award-info":[{"award-number":["Pathos"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001381","name":"National Research Foundation Singapore","doi-asserted-by":"publisher","award":["NRF-CRP14-2014-02"],"award-info":[{"award-number":["NRF-CRP14-2014-02"]}],"id":[{"id":"10.13039\/501100001381","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004211","name":"Oxford Martin School, University of Oxford","doi-asserted-by":"publisher","award":["-"],"award-info":[{"award-number":["-"]}],"id":[{"id":"10.13039\/501100004211","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["-"],"award-info":[{"award-number":["-"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000925","name":"John Templeton Foundation","doi-asserted-by":"publisher","award":["-"],"award-info":[{"award-number":["-"]}],"id":[{"id":"10.13039\/100000925","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011730","name":"Templeton World Charity Foundation","doi-asserted-by":"publisher","award":["-"],"award-info":[{"award-number":["-"]}],"id":[{"id":"10.13039\/501100011730","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Pseudo-density matrices are a generalisation of quantum states and do not obey monogamy of quantum correlations. Could this be the solution to the paradox of information loss during the evaporation of a black hole? In this paper we discuss this possibility, providing a theoretical proposal to extend quantum theory with these pseudo-states to describe the statistics arising in black-hole evaporation. We also provide an experimental demonstration of this theoretical proposal, using a simulation in optical regime, that tomographically reproduces the correlations of the pseudo-density matrix describing this physical phenomenon.<\/jats:p>","DOI":"10.3390\/e22020228","type":"journal-article","created":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T10:10:25Z","timestamp":1582020625000},"page":"228","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Non-Monogamy of Spatio-Temporal Correlations and the Black Hole Information Loss Paradox"],"prefix":"10.3390","volume":"22","author":[{"given":"Chiara","family":"Marletto","sequence":"first","affiliation":[{"name":"Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK"},{"name":"Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore"},{"name":"Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vlatko","family":"Vedral","sequence":"additional","affiliation":[{"name":"Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK"},{"name":"Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore"},{"name":"Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Salvatore","family":"Virz\u00ec","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Torino, via P. 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Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"231301","DOI":"10.1103\/PhysRevLett.116.231301","article-title":"Soft Hair on Black Holes","volume":"116","author":"Hawking","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1140\/epjc\/s10052-016-4553-3","article-title":"Bell violation in the sky","volume":"77","author":"Choudhury","year":"2017","journal-title":"Eur. Phys. J. C"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"063501","DOI":"10.1103\/PhysRevD.96.063501","article-title":"Obstructions to Bell CMB experiments","volume":"96","author":"Martin","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1002\/prop.201500097","article-title":"A model with cosmological Bell inequalities","volume":"64","author":"Maldacena","year":"2016","journal-title":"Fortschr. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1140\/epjc\/s10052-019-7582-x","article-title":"Spectrum of cosmological correlation from vacuum fluctuation of stringy axion in entangled de Sitter space","volume":"80","author":"Choudhury","year":"2020","journal-title":"Eur. Phys. J. C"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1007\/BF01877517","article-title":"Black holes in general relativity","volume":"25","author":"Hawking","year":"1972","journal-title":"Commun. Math. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF02345020","article-title":"Particle creation by black holes","volume":"43","author":"Hawking","year":"1975","journal-title":"Commun. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2460","DOI":"10.1103\/PhysRevD.14.2460","article-title":"Breakdown of predictability in gravitational collapse","volume":"14","author":"Hawking","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"084013","DOI":"10.1103\/PhysRevD.72.084013","article-title":"Information loss in black holes","volume":"72","author":"Hawking","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1098\/rspa.2008.0149","article-title":"Monogamy of non-local quantum correlations","volume":"465","author":"Toner","year":"2009","journal-title":"Proc. R. Soc. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3743","DOI":"10.1103\/PhysRevLett.71.3743","article-title":"Information in black hole radiation","volume":"71","author":"Page","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","unstructured":"Wallace, D. (2017). Why Black Hole information loss is paradoxical. arXiv."},{"key":"ref_16","unstructured":"Misner, C.W., Thorne, K.S., and Wheeler, J.A. (1973). Gravitation, W. H. Freeman and Company."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"18281","DOI":"10.1038\/srep18281","article-title":"Quantum correlations which imply causation","volume":"5","author":"Fitzsimons","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5122","DOI":"10.1103\/PhysRevA.50.5122","article-title":"Theory of two-photon entanglement in type-II optical parametric down-conversion","volume":"50","author":"Rubin","year":"1994","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.physrep.2005.03.003","article-title":"Research On Hidden Variable Theories: A Review Of Recent Progresses","volume":"413","author":"Genovese","year":"2005","journal-title":"Phys. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"010404","DOI":"10.1103\/PhysRevLett.105.010404","article-title":"Statistical Estimation of the Efficiency of Quantum State Tomography Protocols","volume":"105","author":"Bogdanov","year":"2010","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/228\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:58:43Z","timestamp":1760173123000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/228"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,18]]},"references-count":20,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["e22020228"],"URL":"https:\/\/doi.org\/10.3390\/e22020228","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,18]]}}}