{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T03:54:35Z","timestamp":1769745275599,"version":"3.49.0"},"reference-count":38,"publisher":"IOP Publishing","issue":"18","license":[{"start":{"date-parts":[[2020,4,15]],"date-time":"2020-04-15T00:00:00Z","timestamp":1586908800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2020,4,15]],"date-time":"2020-04-15T00:00:00Z","timestamp":1586908800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["PREDICT (PTDC\/CCI-CIF\/29877\/2017)"],"award-info":[{"award-number":["PREDICT (PTDC\/CCI-CIF\/29877\/2017)"]}]},{"DOI":"10.13039\/100010686","name":"H2020 European Institute of Innovation and Technology","doi-asserted-by":"crossref","award":["SPARTA"],"award-info":[{"award-number":["SPARTA"]}],"id":[{"id":"10.13039\/100010686","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["J. Phys. A: Math. Theor."],"published-print":{"date-parts":[[2020,5,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We address the problem of compressing density operators defined on a finite dimensional Hilbert space which assumes a tensor product decomposition. In particular, we look for an\n                    <jats:italic>efficient procedure<\/jats:italic>\n                    for learning the\n                    <jats:italic>most likely<\/jats:italic>\n                    density operator, according to \u2018Jaynes\u2019 principle, given a\n                    <jats:italic>chosen set<\/jats:italic>\n                    of partial information obtained from the unknown quantum system we wish to describe. For complexity reasons, we restrict our analysis to\n                    <jats:italic>tree-structured<\/jats:italic>\n                    sets of bipartite marginals. We focus on the tripartite scenario, where we solve the problem for the couples of measured marginals which are compatible with a quantum Markov chain, providing then an algebraic necessary and sufficient condition for the compatibility to be verified. We introduce the generalization of the procedure to the n-partite scenario, giving some preliminary results. In particular, we prove that if the pairwise Markov condition holds between the subparts then the choice of the\n                    <jats:italic>best<\/jats:italic>\n                    set of tree-structured bipartite marginals can be performed efficiently. Moreover, we provide a new characterization of quantum Markov chains in terms of\n                    <jats:italic>quantum Bayesian updating processes<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1088\/1751-8121\/ab7a52","type":"journal-article","created":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T08:02:56Z","timestamp":1582876976000},"page":"185301","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Recoverability from direct quantum correlations"],"prefix":"10.1088","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4719-1663","authenticated-orcid":false,"given":"S","family":"Di Giorgio","sequence":"first","affiliation":[]},{"given":"P","family":"Mateus","sequence":"additional","affiliation":[]},{"given":"B","family":"Mera","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2020,4,15]]},"reference":[{"key":"aab7a52bib1","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1103\/physrev.106.620","type":"journal-article","article-title":"Information theory and statistical mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"aab7a52bib2","author":"Bishop","year":"2006","type":"book"},{"key":"aab7a52bib3","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1038\/nature23474","type":"journal-article","article-title":"Quantum machine learning","volume":"549","author":"Jacob","year":"2017","journal-title":"Nature"},{"key":"aab7a52bib4","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1080\/00107514.2014.964942","type":"journal-article","article-title":"An introduction to quantum machine learning","volume":"56","author":"Schuld","year":"2015","journal-title":"Contemp. Phys."},{"key":"aab7a52bib5","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1126\/science.aag2302","type":"journal-article","article-title":"Solving the quantum many-body problem with artificial neural networks","volume":"355","author":"Carleo","year":"2017","journal-title":"Science"},{"key":"aab7a52bib6","article-title":"Bayesian networks, causal inference and knowledge discovery","author":"Pearl","year":"2001","type":"book"},{"key":"aab7a52bib7","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/978-1-4612-2404-4_12","type":"book","article-title":"Learning Bayesian networks is NP-complete","author":"Chickering","year":"1996"},{"key":"aab7a52bib8","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/0004-3702(93)90036-b","type":"journal-article","article-title":"Approximating probabilistic inference in Bayesian belief networks is np-hard","volume":"60","author":"Paul","year":"1993","journal-title":"Artif. Intell."},{"key":"aab7a52bib9","first-page":"134","type":"conference-proceedings","article-title":"Learning polytrees","author":"Dasgupta","year":"1999"},{"key":"aab7a52bib10","doi-asserted-by":"publisher","first-page":"462","DOI":"10.1109\/tit.1968.1054142","type":"journal-article","article-title":"Approximating discrete probability distributions with dependence trees","volume":"14","author":"Chow","year":"1968","journal-title":"IEEE Trans. Inf. Theory"},{"key":"aab7a52bib11","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.88.052130","type":"journal-article","article-title":"Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference","volume":"88","author":"Leifer","year":"2013","journal-title":"Phys. Rev. A"},{"key":"aab7a52bib12","doi-asserted-by":"publisher","first-page":"18281","DOI":"10.1038\/srep18281","type":"journal-article","article-title":"Quantum correlations which imply causation","volume":"5","author":"Fitzsimons","year":"2015","journal-title":"Sci. Rep."},{"key":"aab7a52bib13","doi-asserted-by":"publisher","first-page":"20170395","DOI":"10.1098\/rspa.2017.0395","type":"journal-article","article-title":"Can a quantum state over time resemble a quantum state at a single time?","volume":"473","author":"Horsman","year":"2017","journal-title":"Proc. R. Soc. A"},{"key":"aab7a52bib14","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1007\/11830924_40","type":"book","article-title":"Consistency of local density matrices is QMA-complete","author":"Liu","year":"2006"},{"key":"aab7a52bib15","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.98.110503","type":"journal-article","article-title":"Quantum computational complexity of the n-representability problem: Qma complete","volume":"98","author":"Liu","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"aab7a52bib16","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.75.032102","type":"journal-article","article-title":"Compatibility of subsystem states and convex geometry","volume":"75","author":"Hall","year":"2007","journal-title":"Phys. Rev. A"},{"key":"aab7a52bib17","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.90.042314","type":"journal-article","article-title":"Role of correlations in the two-body-marginal problem","volume":"90","author":"Chen","year":"2014","journal-title":"Phys. Rev. A"},{"key":"aab7a52bib18","first-page":"1393","type":"book","article-title":"New outer bounds on the marginal polytope","author":"Sontag","year":"2008"},{"key":"aab7a52bib19","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1140\/epjd\/e2015-60191-7","type":"journal-article","article-title":"Quantum marginal problems","volume":"69","author":"Tyc","year":"2015","journal-title":"Eur. Phys. J. D"},{"key":"aab7a52bib20","article-title":"Quantum states and their marginals: from multipartite entanglement to quantum error-correcting codes","author":"Huber","type":"other"},{"key":"aab7a52bib21","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/978-3-319-78732-9_5","type":"book","author":"Sutter","year":"2018"},{"key":"aab7a52bib22","doi-asserted-by":"publisher","DOI":"10.1063\/1.4769176","type":"journal-article","article-title":"Operator extension of strong subadditivity of entropy","volume":"53","author":"Kim","year":"2012","journal-title":"J. Math. Phys."},{"key":"aab7a52bib23","doi-asserted-by":"publisher","DOI":"10.1063\/1.4823581","type":"journal-article","article-title":"Remarks on Kim\u2019s strong subadditivity matrix inequality: extensions and equality conditions","volume":"54","author":"Ruskai","year":"2013","journal-title":"J. Math. Phys."},{"key":"aab7a52bib24","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1007\/s00220-015-2466-x","type":"journal-article","article-title":"Quantum conditional mutual information and approximate Markov chains","volume":"340","author":"Omar","year":"2015","journal-title":"Commun. Math. Phys."},{"key":"aab7a52bib25","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s00220-004-1049-z","type":"journal-article","article-title":"Structure of states which satisfy strong subadditivity of quantum entropy with equality","volume":"246","author":"Hayden","year":"2004","journal-title":"Commun. Math. Phys."},{"key":"aab7a52bib26","doi-asserted-by":"publisher","first-page":"1938","DOI":"10.1063\/1.1666274","type":"journal-article","article-title":"Proof of the strong subadditivity of quantum-mechanical entropy","volume":"14","author":"Lieb","year":"1973","journal-title":"J. Math. Phys."},{"key":"aab7a52bib27","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/bf01212345","type":"journal-article","article-title":"Sufficient subalgebras and the relative entropy of states of a von neumann algebra","volume":"105","author":"Petz","year":"1986","journal-title":"Commun. Math. Phys."},{"key":"aab7a52bib28","doi-asserted-by":"publisher","first-page":"20150338","DOI":"10.1098\/rspa.2015.0338","type":"journal-article","article-title":"Recoverability in quantum information theory","volume":"471","author":"Wilde","year":"2015","journal-title":"Proc. R. Soc. A"},{"key":"aab7a52bib29","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1142\/s0129055x03001576","type":"journal-article","article-title":"Monotonicity of quantum relative entropy revisited","volume":"15","author":"Petz","year":"2003","journal-title":"Rev. Math. Phys."},{"key":"aab7a52bib30","author":"Kullback","year":"1997","type":"book"},{"key":"aab7a52bib31","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1214\/aoms\/1177699619","type":"journal-article","article-title":"A note on minimum discrimination information","volume":"37","author":"Kullback","year":"1966","journal-title":"Ann. Math. Stat."},{"key":"aab7a52bib32","doi-asserted-by":"publisher","first-page":"664","DOI":"10.3390\/e19120664","type":"journal-article","article-title":"Entropic updating of probabilities and density matrices","volume":"19","author":"Vanslette","year":"2017","journal-title":"Entropy"},{"key":"aab7a52bib33","doi-asserted-by":"publisher","DOI":"10.1088\/2399-6528\/aaaa08","type":"journal-article","article-title":"The quantum Bayes rule and generalizations from the quantum maximum entropy method","volume":"2","author":"Vanslette","year":"2018","journal-title":"J. Phys. Commun."},{"key":"aab7a52bib34","doi-asserted-by":"publisher","first-page":"20150623","DOI":"10.1098\/rspa.2015.0623","type":"journal-article","article-title":"Universal recovery map for approximate Markov chains","volume":"472","author":"Sutter","year":"2016","journal-title":"Proc. R. Soc. A"},{"key":"aab7a52bib35","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.115.050501","type":"journal-article","article-title":"Quantum conditional mutual information, reconstructed states, and state redistribution","volume":"115","author":"Brandao","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"aab7a52bib36","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/bf01646743","type":"journal-article","article-title":"Entropy, information and quantum measurements","volume":"33","author":"Lindblad","year":"1973","journal-title":"Commun. Math. Phys."},{"key":"aab7a52bib37","doi-asserted-by":"publisher","first-page":"5702","DOI":"10.1063\/1.533053","type":"journal-article","article-title":"Monotone Riemannian metrics and relative entropy on noncommutative probability spaces","volume":"40","author":"Lesniewski","year":"1999","journal-title":"Commun. Math. Phys."},{"key":"aab7a52bib38","first-page":"376","type":"journal-article","article-title":"A theorem on trees","volume":"23","author":"Cayley","year":"1889","journal-title":"Quart. J. Math."}],"container-title":["Journal of Physics A: Mathematical and Theoretical"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ab7a52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ab7a52","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ab7a52","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ab7a52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ab7a52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ab7a52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ab7a52","content-type":"text\/html","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ab7a52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T13:55:16Z","timestamp":1768658116000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8121\/ab7a52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,15]]},"references-count":38,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2020,4,15]]},"published-print":{"date-parts":[[2020,5,11]]}},"URL":"https:\/\/doi.org\/10.1088\/1751-8121\/ab7a52","relation":{},"ISSN":["1751-8113","1751-8121"],"issn-type":[{"value":"1751-8113","type":"print"},{"value":"1751-8121","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,15]]},"assertion":[{"value":"Recoverability from direct quantum correlations","name":"article_title","label":"Article Title"},{"value":"Journal of Physics A: Mathematical and Theoretical","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2020 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2019-08-19","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-02-26","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-04-15","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}