{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T15:42:01Z","timestamp":1759160521589},"reference-count":62,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T00:00:00Z","timestamp":1644883200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Steering criteria are conditions whose violation excludes the possibility of describing the observed measurement statistics with local hidden state (LHS) models. When the available data do not allow to exclude arbitrary LHS models, it may still be possible to exclude LHS models with a specific separability structure. Here, we derive experimentally feasible criteria that put quantitative bounds on the multipartite entanglement of LHS. Our results reveal that separable states may contain hidden entanglement that can be unlocked by measurements on another system, even if no steering between the two systems is possible.<\/jats:p>","DOI":"10.22331\/q-2022-02-15-651","type":"journal-article","created":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T17:17:59Z","timestamp":1644945479000},"page":"651","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Entanglement of Local Hidden States"],"prefix":"10.22331","volume":"6","author":[{"given":"Matteo","family":"Fadel","sequence":"first","affiliation":[{"name":"Department of Physics, ETH Z\u00fcrich, 8093 Z\u00fcrich, Switzerland"},{"name":"Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manuel","family":"Gessner","sequence":"additional","affiliation":[{"name":"ICFO-Institut de Ci\u00e8ncies Fot\u00f2niques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels (Barcelona), Spain"},{"name":"Laboratoire Kastler Brossel, ENS-Universit\u00e9 PSL, CNRS, Sorbonne Universit\u00e9, Coll\u00e8ge de France, 24 Rue Lhomond, 75005, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,2,15]]},"reference":[{"key":"0","unstructured":"M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, New York, NY, 2000)."},{"key":"1","doi-asserted-by":"publisher","unstructured":"R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).","DOI":"10.1103\/RevModPhys.81.865"},{"key":"2","doi-asserted-by":"publisher","unstructured":"M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications, Rev. Mod. Phys. 81, 1727 (2009).","DOI":"10.1103\/RevModPhys.81.1727"},{"key":"3","doi-asserted-by":"publisher","unstructured":"N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell Nonlocality, Rev. Mod. Phys. 86, 419 (2014).","DOI":"10.1103\/RevModPhys.86.419"},{"key":"4","doi-asserted-by":"publisher","unstructured":"D. Cavalcanti and P. Skrzypczyk, Quantum steering: a review with focus on semidefinite programming, Rep. Prog. Phys. 80, 024001 (2017).","DOI":"10.1088\/1361-6633\/80\/2\/024001"},{"key":"5","doi-asserted-by":"publisher","unstructured":"N. Friis, G. Vitagliano, M. Malik, and M. Huber, Entanglement certification from theory to experiment, Nat. Rev. Phys. 1, 72 (2019).","DOI":"10.1038\/s42254-018-0003-5"},{"key":"6","doi-asserted-by":"publisher","unstructured":"R. Uola, A. C. S. Costa, H. C. Nguyen, and O. G\u00fchne, Quantum steering, Rev. Mod. Phys. 92, 015001 (2020).","DOI":"10.1103\/RevModPhys.92.015001"},{"key":"7","doi-asserted-by":"publisher","unstructured":"W. D\u00fcr, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62, 062314 (2000).","DOI":"10.1103\/PhysRevA.62.062314"},{"key":"8","doi-asserted-by":"publisher","unstructured":"O. G\u00fchne and G. T\u00f3th, Entanglement Detection, Phys. Rep. 474, 1 (2009).","DOI":"10.1016\/j.physrep.2009.02.004"},{"key":"9","doi-asserted-by":"publisher","unstructured":"F. Levi and F. Mintert, Hierarchies of Multipartite Entanglement, Phys. Rev. Lett. 110, 150402 (2013).","DOI":"10.1103\/PhysRevLett.110.150402"},{"key":"10","unstructured":"M. Walter, D. Gross, J. Eisert, Multi-partite entanglement, arXiv:1612.02437."},{"key":"11","doi-asserted-by":"publisher","unstructured":"S. Szalay, k-stretchability of entanglement, and the duality of k-separability and k-producibility, Quantum 3, 204 (2019).","DOI":"10.22331\/q-2019-12-02-204"},{"key":"12","doi-asserted-by":"crossref","unstructured":"J.-S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).","DOI":"10.1103\/PhysicsPhysiqueFizika.1.195"},{"key":"13","doi-asserted-by":"publisher","unstructured":"H. M. Wiseman, S. J. Jones, and A. C. Doherty, Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox, Phys. Rev. Lett. 98, 140402 (2007).","DOI":"10.1103\/PhysRevLett.98.140402"},{"key":"14","doi-asserted-by":"publisher","unstructured":"R. Gallego and L. Aolita, Resource Theory of Steering, Phys. Rev. X 5, 041008 (2015).","DOI":"10.1103\/PhysRevX.5.041008"},{"key":"15","doi-asserted-by":"publisher","unstructured":"A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Phys. Rev. 47, 777 (1935).","DOI":"10.1103\/PhysRev.47.777"},{"key":"16","doi-asserted-by":"publisher","unstructured":"M. D. Reid, Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification, Phys. Rev. A 40, 913 (1989).","DOI":"10.1103\/PhysRevA.40.913"},{"key":"17","doi-asserted-by":"publisher","unstructured":"B. Yadin, M. Fadel, and M. Gessner, Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox, Nat. Commun. 12, 2401 (2021).","DOI":"10.1038\/s41467-021-22353-3"},{"key":"18","unstructured":"J. Guo, F.-X. Sun, D. Zhu, M. Gessner, Q. He, M. Fadel, Detecting Einstein-Podolsky-Rosen steering in non-Gaussian spin states from conditional spin-squeezing parameters, arXiv:2106.13106."},{"key":"19","doi-asserted-by":"publisher","unstructured":"S. P. Walborn, A. Salles, R. M. Gomes, F. Toscano, and P. H. Souto Ribeiro, Revealing Hidden Einstein-Podolsky-Rosen Nonlocality, Phys. Rev. Lett. 106, 130402 (2013).","DOI":"10.1103\/PhysRevLett.106.130402"},{"key":"20","doi-asserted-by":"publisher","unstructured":"J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti and J. C. Howell, Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations, Phys. Rev. A 87, 062103 (2013).","DOI":"10.1103\/PhysRevA.87.062103"},{"key":"21","doi-asserted-by":"publisher","unstructured":"A. C. S. Costa, R. Uola, O. G\u00fchne, Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems, Entropy 20, 763 (2018).","DOI":"10.3390\/e20100763"},{"key":"22","doi-asserted-by":"publisher","unstructured":"A. Riccardi, C. Macchiavello, and L. Maccone, Multipartite steering inequalities based on entropic uncertainty relations, Phys. Rev. A 97, 052307 (2018).","DOI":"10.1103\/PhysRevA.97.052307"},{"key":"23","doi-asserted-by":"publisher","unstructured":"Q. Y. He and M. D. Reid, Genuine Multipartite Einstein-Podolsky-Rosen Steering, Phys. Rev. Lett. 111, 250403 (2013).","DOI":"10.1103\/PhysRevLett.111.250403"},{"key":"24","doi-asserted-by":"publisher","unstructured":"M. D. Reid, Monogamy inequalities for the Einstein-Podolsky-Rosen paradox and quantum steering, Phys. Rev. A 88, 062108 (2013).","DOI":"10.1103\/PhysRevA.88.062108"},{"key":"25","doi-asserted-by":"publisher","unstructured":"R. Y. Teh and M. D. Reid, Criteria for genuine N-partite continuous-variable entanglement and Einstein-Podolsky-Rosen steering, Phys. Rev. A 90, 062337 (2014).","DOI":"10.1103\/PhysRevA.90.062337"},{"key":"26","doi-asserted-by":"publisher","unstructured":"S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, P. K. Lam, Multipartite Einstein\u2013Podolsky\u2013Rosen steering and genuine tripartite entanglement with optical networks, Nature Phys. 11, 167 (2015).","DOI":"10.1038\/nphys3202"},{"key":"27","doi-asserted-by":"publisher","unstructured":"D. Cavalcanti, P. Skrzypczyk, G. H. Aguilar, R. V. Nery, P.H. Souto Ribeiro, S. P. Walborn, Detection of entanglement in asymmetric quantum networks and multipartite quantum steering, Nat. Commun. 6, 7941 (2015).","DOI":"10.1038\/ncomms8941"},{"key":"28","doi-asserted-by":"publisher","unstructured":"Y. Xiang, X. Su, L. Mi\u0161ta, Jr., G. Adesso, and Q. He, Multipartite Einstein-Podolsky-Rosen steering sharing with separable states, Phys. Rev. A 99, 010104(R) (2019).","DOI":"10.1103\/PhysRevA.99.010104"},{"key":"29","doi-asserted-by":"publisher","unstructured":"S. L. Braunstein and C. M. Caves, Statistical Distance and the Geometry of Quantum States, Phys. Rev. Lett. 72, 3439 (1994).","DOI":"10.1103\/PhysRevLett.72.3439"},{"key":"30","doi-asserted-by":"publisher","unstructured":"V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nature Phot. 5, 222 (2011).","DOI":"10.1038\/nphoton.2011.35"},{"key":"31","doi-asserted-by":"publisher","unstructured":"G. T\u00f3th and I. Apellaniz, Quantum metrology from a quantum information science perspective, J. Phys. A 47, 424006 (2014).","DOI":"10.1088\/1751-8113\/47\/42\/424006"},{"key":"32","unstructured":"L. Pezz\u00e8 and A. Smerzi, Quantum theory of phase estimation, in Atom Interferometry, Proceedings of the International School of Physics ``Enrico Fermi&apos;&apos;, Course 188, Varenna, edited by G. M. Tino and M. A. Kasevich (IOS Press, Amsterdam) p. 691 (2014)."},{"key":"33","unstructured":"See the Supplemental Material for a proof of Eq. (3)."},{"key":"34","doi-asserted-by":"publisher","unstructured":"M. Gessner, L. Pezz\u00e8, A. Smerzi, Efficient entanglement criteria for discrete, continuous, and hybrid variables, Phys. Rev. A 94, 020101(R) (2016).","DOI":"10.1103\/PhysRevA.94.020101"},{"key":"35","doi-asserted-by":"publisher","unstructured":"O. Cohen, Unlocking Hidden Entanglement with Classical Information, Phys. Rev. Lett. 80, 2493 (1998).","DOI":"10.1103\/PhysRevLett.80.2493"},{"key":"36","doi-asserted-by":"publisher","unstructured":"O. Cohen, Unlocking Hidden Entanglement with Classical Information, Phys. Rev. A 60, 80 (1999).","DOI":"10.1103\/PhysRevA.60.80"},{"key":"37","doi-asserted-by":"publisher","unstructured":"D. M. Greenberger, M. A. Horne, and A. Zeilinger, Going Beyond Bell&apos;s Theorem, in ``Bell&apos;s Theorem, Quantum Theory, and Conceptions of the Universe&apos;&apos;, M. Kafatos (Ed.), Kluwer, Dordrecht, pp. 69 (1989).","DOI":"10.1007\/978-94-017-0849-4_10"},{"key":"38","doi-asserted-by":"publisher","unstructured":"H. F. Hofmann and S. Takeuchi, Violation of local uncertainty relations as a signature of entanglement, Phys. Rev. A 68, 6 (2003).","DOI":"10.1103\/PhysRevA.68.032103"},{"key":"39","doi-asserted-by":"publisher","unstructured":"M. Fadel and M. Gessner, Relating spin squeezing to multipartite entanglement criteria for particles and modes, Phys. Rev. A 102, 012412 (2020).","DOI":"10.1103\/PhysRevA.102.012412"},{"key":"40","doi-asserted-by":"publisher","unstructured":"M. Gessner, L. Pezz\u00e8, and A. Smerzi, Entanglement and squeezing in continuous-variable systems, Quantum 1, 17 (2017).","DOI":"10.22331\/q-2017-07-14-17"},{"key":"41","doi-asserted-by":"publisher","unstructured":"O. G\u00fchne, G. T\u00f3th anf H. Briegel, Multipartite entanglement in spin chains, New J. Phys. 7, 229 (2005).","DOI":"10.1088\/1367-2630\/7\/1\/229"},{"key":"42","doi-asserted-by":"publisher","unstructured":"Z. Ren, W. Li, A. Smerzi, and M. Gessner, Metrological Detection of Multipartite Entanglement from Young Diagrams, Phys. Rev. Lett. 126, 080502 (2021).","DOI":"10.1103\/PhysRevLett.126.080502"},{"key":"43","doi-asserted-by":"publisher","unstructured":"P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezz\u00e8, and A. Smerzi, Fisher information and multiparticle entanglement, Phys. Rev. A 85, 022321 (2012).","DOI":"10.1103\/PhysRevA.85.022321"},{"key":"44","doi-asserted-by":"publisher","unstructured":"G. T\u00f3th, Multipartite entanglement and high-precision metrology, Phys. Rev. A 85, 022322 (2012).","DOI":"10.1103\/PhysRevA.85.022322"},{"key":"45","doi-asserted-by":"publisher","unstructured":"V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006).","DOI":"10.1103\/PhysRevLett.96.010401"},{"key":"46","doi-asserted-by":"publisher","unstructured":"M. Gessner and A. Smerzi, Encrypted quantum correlations: Delayed choice of quantum statistics and other applications, EPJ Quantum Technol. 6, 4 (2019).","DOI":"10.1140\/epjqt\/s40507-019-0074-y"},{"key":"47","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":"48","doi-asserted-by":"publisher","unstructured":"A. K. Ekert, Quantum cryptography based on Bell\u2019s theorem, Phys. Rev. Lett. 67, 661 (1991).","DOI":"10.1103\/PhysRevLett.67.661"},{"key":"49","doi-asserted-by":"publisher","unstructured":"V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Quantifying Entanglement, Phys. Rev. Lett. 78, 2275 (1997).","DOI":"10.1103\/PhysRevLett.78.2275"},{"key":"50","doi-asserted-by":"publisher","unstructured":"A. Ac\u00edn, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Device-Independent Security of Quantum Cryptography against Collective Attacks, Phys. Rev. Lett. 98, 230501 (2007).","DOI":"10.1103\/PhysRevLett.98.230501"},{"key":"51","doi-asserted-by":"publisher","unstructured":"B. Morris, B. Yadin, M. Fadel, T. Zibold, P. Treutlein and G. Adesso, Entanglement between identical particles is a useful and consistent resource, Phys. Rev. X 10, 041012 (2020).","DOI":"10.1103\/PhysRevX.10.041012"},{"key":"52","doi-asserted-by":"publisher","unstructured":"M. Fadel, A. Usui, M. Huber, N. Friis and G. Vitagliano, Entanglement Quantification in Atomic Ensembles, Phys. Rev. Lett. 127, 010401 (2021).","DOI":"10.1103\/PhysRevLett.127.010401"},{"key":"53","doi-asserted-by":"publisher","unstructured":"H. Strobel, W. Muessel, D. Linnemann, T. Zibold, D. B. Hume, L. Pezz\u00e8, A. Smerzi, and M. K. Oberthaler, Fisher information and entanglement of non-Gaussian spin states, Science 345, 424 (2014).","DOI":"10.1126\/science.1250147"},{"key":"54","doi-asserted-by":"publisher","unstructured":"M. Fadel, T. Zibold, B. D\u00e9camps and P. Treutlein, Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates, Science 360, 409 (2018).","DOI":"10.1126\/science.aao1850"},{"key":"55","doi-asserted-by":"publisher","unstructured":"P. Kunkel, M. Pr\u00fcfer, H. Strobel, D. Linnemann, A. Fr\u00f6lian, T. Gasenzer, M. G\u00e4rttner and M. K. Oberthaler, Spatially distributed multipartite entanglement enables EPR steering of atomic clouds, Science 360, 413 (2018).","DOI":"10.1126\/science.aao2254"},{"key":"56","doi-asserted-by":"publisher","unstructured":"K. Lange, J. Peise, B. L\u00fccke, I. Kruse, G. Vitagliano, I. Apellaniz, M. Kleinmann, G. T\u00f3th and C. Klempt, Entanglement between two spatially separated atomic modes, Science 360, 416 (2018).","DOI":"10.1126\/science.aao2035"},{"key":"57","doi-asserted-by":"publisher","unstructured":"J. G. Bohnet, B. C. Sawyer, J. W. Britton, M. L. Wall, A. M. Rey, M. Foss-Feig, J. J. Bollinger, Quantum spin dynamics and entanglement generation with hundreds of trapped ions, Science 352, 1297 (2016).","DOI":"10.1126\/science.aad9958"},{"key":"58","doi-asserted-by":"publisher","unstructured":"Z. Qin, M. Gessner, Z. Ren, X. Deng, D. Han, W. Li, X. Su, A. Smerzi, and K. Peng, Characterizing the multipartite continuous-variable entanglement structure from squeezing coefficients and the Fisher information, npj Quant. Inf. 5, 3 (2019).","DOI":"10.1038\/s41534-018-0119-6"},{"key":"59","doi-asserted-by":"publisher","unstructured":"R. Takagi and Q. Zhuang, Convex resource theory of non-Gaussianity, Phys. Rev. A 97, 062337 (2018).","DOI":"10.1103\/PhysRevA.97.062337"},{"key":"60","doi-asserted-by":"publisher","unstructured":"F. Albarelli, M. G. Genoni, M. G. A. Paris, and A. Ferraro, Resource theory of quantum non-Gaussianity and Wigner negativity, Phys. Rev. A 98, 052350 (2018).","DOI":"10.1103\/PhysRevA.98.052350"},{"key":"61","doi-asserted-by":"publisher","unstructured":"A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: Quantum coherence as a resource, Rev. Mod. Phys. 89, 041003 (2017).","DOI":"10.1103\/RevModPhys.89.041003"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-02-15-651\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T17:18:05Z","timestamp":1644945485000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-02-15-651\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,15]]},"references-count":62,"URL":"https:\/\/doi.org\/10.22331\/q-2022-02-15-651","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,15]]},"article-number":"651"}}