{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T07:12:04Z","timestamp":1766301124225,"version":"3.40.5"},"reference-count":70,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T00:00:00Z","timestamp":1746489600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12475087"],"award-info":[{"award-number":["12475087"]}],"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":["12235008"],"award-info":[{"award-number":["12235008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"crossref","award":["2024M753174"],"award-info":[{"award-number":["2024M753174"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["null"],"award-info":[{"award-number":["null"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"We propose in this work a practical approach to address the longstanding and challenging problem of quantum separability, leveraging the correlation matrices of generic observables. General separability conditions are obtained by dint of constructing the measurement-induced Bloch space, which in essence come from the intrinsic constraints in the space of quantum state. The novel approach can not only reproduce various established entanglement criteria, it may as well brings about some new results, possessing obvious advantages for certain bound entangled states and the high dimensional Werner states. Moreover, it is found that criteria obtained in our approach can be directly transformed into entanglement witness operators.<\/jats:p>","DOI":"10.22331\/q-2025-05-06-1734","type":"journal-article","created":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T15:34:37Z","timestamp":1746545677000},"page":"1734","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["An Effective Way to Determine the Separability of Quantum State"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4122-4310","authenticated-orcid":false,"given":"Ma-Cheng","family":"Yang","sequence":"first","affiliation":[{"name":"School of Physical Sciences, University of Chinese Academy of Sciences, YuQuan Road 19A, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9174-7307","authenticated-orcid":false,"given":"Cong-Feng","family":"Qiao","sequence":"additional","affiliation":[{"name":"School of Physical Sciences, University of Chinese Academy of Sciences, YuQuan Road 19A, Beijing 100049, China"},{"name":"Key Laboratory of Vacuum Physics, CAS, YuQuan Road 19A, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,5,6]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Vlatko Vedral. ``Quantum entanglement''. Nat. Phys. 10, 256\u2013258 (2014).","DOI":"10.1038\/nphys2904"},{"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":"Otfried G\u00fchne and G\u00e9za T\u00f3th. ``Entanglement detection''. Phys. Rep. 474, 1\u201375 (2009).","DOI":"10.1016\/j.physrep.2009.02.004"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Leonid Gurvits. ``Classical complexity and quantum entanglement''. J Comput Syst Sci 69, 448\u2013484 (2004).","DOI":"10.1016\/j.jcss.2004.06.003"},{"key":"4","doi-asserted-by":"publisher","unstructured":"M. Horodecki, P. Horodecki, and R. Horodecki. ``Separability of mixed states: Necessary and sufficient conditions''. Phys. Lett. A 223, 1\u20138 (1996).","DOI":"10.1016\/S0375-9601(96)00706-2"},{"key":"5","doi-asserted-by":"publisher","unstructured":"A. Peres. ``Separability criterion for density matrices''. Phys. Rev. Lett. 77, 1413 (1996).","DOI":"10.1103\/PhysRevLett.77.1413"},{"key":"6","doi-asserted-by":"publisher","unstructured":"M. Horodecki, P. Horodecki, and R. Horodecki. ``Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps''. Phys. Lett. A 283, 1\u20137 (2001).","DOI":"10.1016\/S0375-9601(01)00142-6"},{"key":"7","doi-asserted-by":"publisher","unstructured":"A. Sorensen, L. M. Duan, J. I. Cirac, and P. Zoller. ``Many-particle entanglement with bose-einstein condensates''. Nature 409, 63\u201366 (2001).","DOI":"10.1038\/35051038"},{"key":"8","doi-asserted-by":"publisher","unstructured":"G. Toth, C. Knapp, O. Guhne, and H. J. Briegel. ``Optimal spin squeezing inequalities detect bound entanglement in spin models''. Phys. Rev. Lett. 99, 250405 (2007).","DOI":"10.1103\/PhysRevLett.99.250405"},{"key":"9","doi-asserted-by":"publisher","unstructured":"G\u00e9za T\u00f3th, Christian Knapp, Otfried G\u00fchne, and Hans J. Briegel. ``Spin squeezing and entanglement''. Phys. Rev. A 79, 042334 (2009).","DOI":"10.1103\/PhysRevA.79.042334"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Jian Ma, Xiaoguang Wang, C. P. Sun, and Franco Nori. ``Quantum spin squeezing''. Phys. Rep. 509, 89 (2011).","DOI":"10.1016\/j.physrep.2011.08.003"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Oliver Rudolph. ``A separability criterion for density operators''. J. Phys. A 33, 3951\u20133955 (2000).","DOI":"10.1088\/0305-4470\/33\/21\/308"},{"key":"12","doi-asserted-by":"publisher","unstructured":"Kai Chen and Ling-An Wu. ``A matrix realignment method for recognizing entanglement''. Quantum Inf. Comput. 3, 193\u2013202 (2003).","DOI":"10.26421\/QIC3.3-1"},{"key":"13","doi-asserted-by":"publisher","unstructured":"O. Rudolph. ``Further results on the cross norm criterion for separability''. Quantum Inf. Process. 4, 219\u2013239 (2005).","DOI":"10.1007\/s11128-005-5664-1"},{"key":"14","doi-asserted-by":"publisher","unstructured":"Julio I. de Vicente. ``Separability criteria based on the Bloch representation of density matrices''. Quantum Inf. Comput. 7, 624 (2007).","DOI":"10.26421\/QIC7.7-5"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Julio I. de Vicente. ``Further results on entanglement detection and quantification from the correlation matrix criterion''. J. Phys. A: Math. Theor. 41, 065309 (2008).","DOI":"10.1088\/1751-8113\/41\/6\/065309"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Jun-Li Li and Cong-Feng Qiao. ``A necessary and sufficient criterion for the separability of quantum state''. Sci. Rep. 8, 1442 (2018).","DOI":"10.1038\/s41598-018-19709-z"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Jiangwei Shang, Ali Asadian, Huangjun Zhu, and Otfried G\u00fchne. ``Enhanced entanglement criterion via symmetric informationally complete measurements''. Phys. Rev. A 98, 022309 (2018).","DOI":"10.1103\/PhysRevA.98.022309"},{"key":"18","doi-asserted-by":"publisher","unstructured":"Gniewomir Sarbicki, Giovanni Scala, and Dariusz Chru\u015bci\u0144ski. ``Family of multipartite separability criteria based on a correlation tensor''. Phys. Rev. A 101, 012341 (2020).","DOI":"10.1103\/PhysRevA.101.012341"},{"key":"19","doi-asserted-by":"publisher","unstructured":"L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller. ``Inseparability criterion for continuous variable systems''. Phys. Rev. Lett. 84, 2722 (2000).","DOI":"10.1103\/PhysRevLett.84.2722"},{"key":"20","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, 032103 (2003).","DOI":"10.1103\/PhysRevA.68.032103"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Otfried G\u00fchne. ``Characterizing entanglement via uncertainty relations''. Phys. Rev. Lett. 92, 117903 (2004).","DOI":"10.1103\/PhysRevLett.92.117903"},{"key":"22","doi-asserted-by":"publisher","unstructured":"C. J. Zhang, Y. S. Zhang, S. Zhang, and G. C. Guo. ``Optimal entanglement witnesses based on local orthogonal observables''. Phys. Rev. A 76, 012334 (2007).","DOI":"10.1103\/PhysRevA.76.012334"},{"key":"23","doi-asserted-by":"publisher","unstructured":"C. J. Zhang, H. Nha, Y. S. Zhang, and G. C. Guo. ``Entanglement detection via tighter local uncertainty relations''. Phys. Rev. A 81, 012324 (2010).","DOI":"10.1103\/PhysRevA.81.012324"},{"key":"24","doi-asserted-by":"publisher","unstructured":"R. Schwonnek, L. Dammeier, and R. F. Werner. ``State-independent uncertainty relations and entanglement detection in noisy systems''. Phys. Rev. Lett. 119, 170404 (2017).","DOI":"10.1103\/PhysRevLett.119.170404"},{"key":"25","doi-asserted-by":"publisher","unstructured":"O. G\u00fchne, P. Hyllus, O. Gittsovich, and J. Eisert. ``Covariance matrices and the separability problem''. Phys. Rev. Lett. 99, 130504 (2007).","DOI":"10.1103\/PhysRevLett.99.130504"},{"key":"26","doi-asserted-by":"publisher","unstructured":"O. Gittsovich, O. G\u00fchne, P. Hyllus, and J. Eisert. ``Unifying several separability conditions using the covariance matrix criterion''. Phys. Rev. A 78, 052319 (2008).","DOI":"10.1103\/PhysRevA.78.052319"},{"key":"27","doi-asserted-by":"publisher","unstructured":"P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezze, and A. Smerzi. ``Fisher information and multiparticle entanglement''. Phys. Rev. A 85, 022321 (2012).","DOI":"10.1103\/PhysRevA.85.022321"},{"key":"28","doi-asserted-by":"publisher","unstructured":"N. Li and S. L. Luo. ``Entanglement detection via quantum Fisher information''. Phys. Rev. A 88, 014301 (2013).","DOI":"10.1103\/PhysRevA.88.014301"},{"key":"29","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":"30","doi-asserted-by":"publisher","unstructured":"Ao-Xiang Liu, Ma-Cheng Yang, and Cong-Feng Qiao. ``Entanglement criteria based on quantum fisher information''. Phys. Lett. A 527, 130003 (2024).","DOI":"10.1016\/j.physleta.2024.130003"},{"key":"31","doi-asserted-by":"publisher","unstructured":"E. Shchukin and W. Vogel. ``Inseparability criteria for continuous bipartite quantum states''. Phys. Rev. Lett. 95, 230502 (2005).","DOI":"10.1103\/PhysRevLett.95.230502"},{"key":"32","doi-asserted-by":"publisher","unstructured":"A. Elben, R. Kueng, H. R. Huang, R. van Bijnen, C. Kokail, M. Dalmonte, P. Calabrese, B. Kraus, J. Preskill, P. Zoller, and B. Vermersch. ``Mixed-state entanglement from local randomized measurements''. Phys. Rev. Lett. 125, 200501 (2020).","DOI":"10.1103\/PhysRevLett.125.200501"},{"key":"33","doi-asserted-by":"publisher","unstructured":"Antoine Neven, Jose Carrasco, Vittorio Vitale, Christian Kokail, Andreas Elben, Marcello Dalmonte, Pasquale Calabrese, Peter Zoller, Beno\u0131\u0302t Vermersch, Richard Kueng, and Barbara Kraus. ``Symmetry-resolved entanglement detection using partial transpose moments''. NPJ Quantum Inf. 7, 1\u201312 (2021).","DOI":"10.1038\/s41534-021-00487-y"},{"key":"34","doi-asserted-by":"publisher","unstructured":"X. D. Yu, S. Imai, and O. Guhne. ``Optimal entanglement certification from moments of the partial transpose''. Phys. Rev. Lett. 127, 060504 (2021).","DOI":"10.1103\/PhysRevLett.127.060504"},{"key":"35","doi-asserted-by":"publisher","unstructured":"U. Fano. ``Description of states in quantum mechanics by density matrix and operator techniques''. Rev. Mod. Phys. 29, 74 (1957).","DOI":"10.1103\/RevModPhys.29.74"},{"key":"36","doi-asserted-by":"publisher","unstructured":"John E. Harriman. ``Geometry of density matrices. i. definitions, $n$ matrices and $1$ matrices''. Phys. Rev. A 17, 1249 (1978).","DOI":"10.1103\/PhysRevA.17.1249"},{"key":"37","doi-asserted-by":"publisher","unstructured":"F. T. Hioe and J. H. Eberly. ``N-level coherence vector and higher conservation laws in quantum optics and quantum mechanics''. Phys. Rev. Lett. 47, 838 (1981).","DOI":"10.1103\/PhysRevLett.47.838"},{"key":"38","doi-asserted-by":"publisher","unstructured":"M. S. Byrd and N. Khaneja. ``Characterization of the positivity of the density matrix in terms of the coherence vector representation''. Phys. Rev. A 68, 062322 (2003).","DOI":"10.1103\/PhysRevA.68.062322"},{"key":"39","doi-asserted-by":"publisher","unstructured":"Gen Kimura. ``The bloch vector for n-level systems''. Phys. Lett. A 314, 339\u2013349 (2003).","DOI":"10.1016\/s0375-9601(03)00941-1"},{"key":"40","doi-asserted-by":"publisher","unstructured":"Jun-Li Li and Cong-Feng Qiao. ``Reformulating the quantum uncertainty relation''. Sci. Rep. 5, 12708 (2015).","DOI":"10.1038\/srep12708"},{"key":"41","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":"42","doi-asserted-by":"publisher","unstructured":"E. Schr\u00f6dinger. ``Discussion of probability relations between separated systems''. Math. Proc. Cambridge Philos. Soc. 31, 555\u2013563 (1935).","DOI":"10.1017\/s0305004100013554"},{"key":"43","doi-asserted-by":"publisher","unstructured":"J. S. Bell. ``On the Einstein Podolsky Rosen paradox''. Physics Physique Fizika 1, 195 (1964).","DOI":"10.1142\/9789812795854_0072"},{"key":"44","doi-asserted-by":"publisher","unstructured":"John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt. ``Proposed experiment to test local hidden-variable theories''. Phys. Rev. Lett. 23, 880 (1969).","DOI":"10.1103\/PhysRevLett.23.880"},{"key":"45","doi-asserted-by":"publisher","unstructured":"Stuart J. Freedman and John F. Clauser. ``Experimental test of local hidden-variable theories''. Phys. Rev. Lett. 28, 938 (1972).","DOI":"10.1103\/PhysRevLett.28.938"},{"key":"46","doi-asserted-by":"publisher","unstructured":"Alain Aspect, Philippe Grangier, and G\u00e9rard Roger. ``Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: A new violation of Bell's inequalities''. Phys. Rev. Lett. 49, 91 (1982).","DOI":"10.1103\/PhysRevLett.49.91"},{"key":"47","doi-asserted-by":"publisher","unstructured":"Alain Aspect, Jean Dalibard, and G\u00e9rard Roger. ``Experimental test of Bell's inequalities using time- varying analyzers''. Phys. Rev. Lett. 49, 1804 (1982).","DOI":"10.1103\/PhysRevLett.49.1804"},{"key":"48","doi-asserted-by":"publisher","unstructured":"M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland. ``Experimental violation of a Bell's inequality with efficient detection''. Nature 409, 791\u2013794 (2001).","DOI":"10.1038\/35057215"},{"key":"49","doi-asserted-by":"publisher","unstructured":"B. Hensen, H. Bernien, A. E. Dreau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellan, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson. ``Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres''. Nature 526, 682\u2013686 (2015).","DOI":"10.1038\/nature15759"},{"key":"50","doi-asserted-by":"publisher","unstructured":"J. Handsteiner, A. S. Friedman, D. Rauch, J. Gallicchio, B. Liu, H. Hosp, J. Kofler, D. Bricher, M. Fink, C. Leung, A. Mark, H. T. Nguyen, I. Sanders, F. Steinlechner, R. Ursin, S. Wengerowsky, A. H. Guth, D. I. Kaiser, T. Scheidl, and A. Zeilinger. ``Cosmic Bell Test: Measurement settings from milky way stars''. Phys. Rev. Lett. 118, 060401 (2017).","DOI":"10.1103\/PhysRevLett.118.060401"},{"key":"51","doi-asserted-by":"publisher","unstructured":"B. I. G. Bell Test Collaboration. ``Challenging local realism with human choices''. Nature 557, 212\u2013216 (2018).","DOI":"10.1038\/s41586-018-0085-3"},{"key":"52","doi-asserted-by":"publisher","unstructured":"R. F. Werner. ``Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model''. Phys. Rev. A 40, 4277 (1989).","DOI":"10.1103\/physreva.40.4277"},{"key":"53","doi-asserted-by":"publisher","unstructured":"Konrad Szyma\u0144ski, Stephan Weis, and Karol \u017byczkowski. ``Classification of joint numerical ranges of three hermitian matrices of size three''. Linear Algebra Appl 545, 148\u2013173 (2018).","DOI":"10.1016\/j.laa.2017.11.017"},{"key":"54","doi-asserted-by":"publisher","unstructured":"Konrad Szyma\u0144ski and Karol \u017byczkowski. ``Geometric and algebraic origins of additive uncertainty relations''. J. Phys. A: Math. Theor. 53, 015302 (2020).","DOI":"10.1088\/1751-8121\/ab4543"},{"key":"55","doi-asserted-by":"publisher","unstructured":"Zhen-Peng Xu, Ren\u00e9 Schwonnek, and Andreas Winter. ``Bounding the joint numerical range of pauli strings by graph parameters''. PRX Quantum 5, 020318 (2024).","DOI":"10.1103\/PRXQuantum.5.020318"},{"key":"56","doi-asserted-by":"publisher","unstructured":"Carlos de Gois, Kiara Hansenne, and Otfried G\u00fchne. ``Uncertainty relations from graph theory''. Phys. Rev. A 107, 062211 (2023).","DOI":"10.1103\/PhysRevA.107.062211"},{"key":"57","doi-asserted-by":"publisher","unstructured":"Mois\u00e9s Bermejo Mor\u00e1n and Felix Huber. ``Uncertainty relations from state polynomial optimization''. Phys. Rev. Lett. 132, 200202 (2024).","DOI":"10.1103\/PhysRevLett.132.200202"},{"key":"58","doi-asserted-by":"publisher","unstructured":"O. Rudolph. ``Some properties of the computable cross-norm criterion for separability''. Phys. Rev. A 67, 032312 (2003).","DOI":"10.1103\/PhysRevA.67.032312"},{"key":"59","doi-asserted-by":"publisher","unstructured":"Ma-Cheng Yang, Jun-Li Li, and Cong-Feng Qiao. ``The decompositions of werner and isotropic states''. Quantum Inf. Process. 20 (2021).","DOI":"10.1007\/s11128-021-03193-y"},{"key":"60","doi-asserted-by":"publisher","unstructured":"F. Verstraete, J. Dehaene, and B. De Moor. ``Normal forms and entanglement measures for multipartite quantum states''. Phys. Rev. A 68, 012103 (2003).","DOI":"10.1103\/PhysRevA.68.012103"},{"key":"61","doi-asserted-by":"publisher","unstructured":"Jun-Li Li and Cong-Feng Qiao. ``Separable decompositions of bipartite mixed states''. Quantum Inf. Process. 17, 92 (2018).","DOI":"10.1007\/s11128-018-1862-5"},{"key":"62","doi-asserted-by":"publisher","unstructured":"B. M. Terhal. ``Detecting quantum entanglement''. Theor Comput Sci 287, 313\u2013335 (2002).","DOI":"10.1016\/S0304-3975(02)00139-1"},{"key":"63","unstructured":"David S. Dummit and Richard M. Foote. ``Abstract algebra''. Wiley. (2003). url: https:\/\/archive.org\/details\/abstractalgebra0000dumm\/page\/n9\/mode\/2up."},{"key":"64","doi-asserted-by":"publisher","unstructured":"Roger A Horn and Charles R Johnson. ``Matrix analysis''. Cambridge University Press. (2013).","DOI":"10.1017\/CBO9781139020411"},{"key":"65","doi-asserted-by":"publisher","unstructured":"R. Penrose. ``A generalized inverse for matrices''. Math. Proc. Cambridge Philos. Soc. 51, 406\u2013413 (1955).","DOI":"10.1017\/s0305004100030401"},{"key":"66","doi-asserted-by":"publisher","unstructured":"Boyd, Vandenberghe, and Faybusovich. ``Convex optimization''. IEEE Trans. Autom. Control 51 (2006).","DOI":"10.1017\/CBO9780511804441"},{"key":"67","doi-asserted-by":"publisher","unstructured":"P. Horodecki. ``Separability criterion and inseparable mixed states with positive partial transposition''. Phys. Lett. A 232, 333\u2013339 (1997).","DOI":"10.1016\/S0375-9601(97)00416-7"},{"key":"68","doi-asserted-by":"publisher","unstructured":"Charles H. Bennett, David P. DiVincenzo, Tal Mor, Peter W. Shor, John A. Smolin, and Barbara M. Terhal. ``Unextendible product bases and bound entanglement''. Phys. Rev. Lett. 82, 5385 (1999).","DOI":"10.1103\/PhysRevLett.82.5385"},{"key":"69","doi-asserted-by":"publisher","unstructured":"Dagmar Bru\u00df and Asher Peres. ``Construction of quantum states with bound entanglement''. Phys. Rev. A 61, 030301 (2000).","DOI":"10.1103\/PhysRevA.61.030301"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2025-05-06-1734\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T15:35:38Z","timestamp":1746545738000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2025-05-06-1734\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,6]]},"references-count":70,"URL":"https:\/\/doi.org\/10.22331\/q-2025-05-06-1734","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,6]]},"article-number":"1734"}}