{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T21:05:14Z","timestamp":1771967114285,"version":"3.50.1"},"reference-count":45,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T00:00:00Z","timestamp":1672272000000},"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>Spin squeezing inequalities (SSI) represent a major tool to probe quantum entanglement among a collection of few-level atoms, and are based on collective spin measurements and their fluctuations. Yet, for atomic ensembles of spin-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>j<\/mml:mi><\/mml:math> atoms and ultracold spinor gases, many experiments can image the populations in all Zeeman sublevels <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>s<\/mml:mi><mml:mo>=<\/mml:mo><mml:mo>&amp;#x2212;<\/mml:mo><mml:mi>j<\/mml:mi><mml:mo>,<\/mml:mo><mml:mo>&amp;#x2212;<\/mml:mo><mml:mi>j<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mo>&amp;#x2026;<\/mml:mo><mml:mo>,<\/mml:mo><mml:mi>j<\/mml:mi><\/mml:math>, potentially revealing finer features of quantum entanglement not captured by SSI. Here we present a systematic approach which exploits Zeeman-sublevel population measurements in order to construct novel entanglement criteria, and illustrate our approach on ground states of spin-1 and spin-2 Bose-Einstein condensates. Beyond these specific examples, our approach allows one to infer, in a systematic manner, the optimal permutationally-invariant entanglement witness for any given set of collective measurements in an ensemble of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><\/mml:math>-level quantum systems.<\/jats:p>","DOI":"10.22331\/q-2022-12-29-887","type":"journal-article","created":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T15:40:16Z","timestamp":1672328416000},"page":"887","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities"],"prefix":"10.22331","volume":"6","author":[{"given":"Guillem","family":"M\u00fcller-Rigat","sequence":"first","affiliation":[{"name":"ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maciej","family":"Lewenstein","sequence":"additional","affiliation":[{"name":"ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"},{"name":"ICREA, Pg. Llu\u00eds Companys 23, 08010 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7703-8539","authenticated-orcid":false,"given":"Ir\u00e9n\u00e9e","family":"Fr\u00e9rot","sequence":"additional","affiliation":[{"name":"Univ Grenoble Alpes, CNRS, Grenoble INP, Institut N\u00e9el, 38000 Grenoble, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,12,29]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"P. Bataille, A. Litvinov, I. Manai, J. Huckans, F. Wiotte, A. Kaladjian, O. Gorceix, E. Mar\u00e9chal, B. Laburthe-Tolra, and M. Robert-de Saint-Vincent. Adiabatic spin-dependent momentum transfer in an su($n$) degenerate fermi gas. Phys. Rev. A, 102: 013317, Jul 2020. 10.1103\/PhysRevA.102.013317. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevA.102.013317.","DOI":"10.1103\/PhysRevA.102.013317"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Rohit Prasad Bhatt, Jan Kilinc, Lilo H\u00f6cker, and Fred Jendrzejewski. Stochastic dynamics of a few sodium atoms in presence of a cold potassium cloud. Scientific Reports, 12 (1), Feb 2022. ISSN 2045-2322. 10.1038\/s41598-022-05778-8. URL http:\/\/dx.doi.org\/10.1038\/s41598-022-05778-8.","DOI":"10.1038\/s41598-022-05778-8"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Thomas Chalopin, Chayma Bouazza, Alexandre Evrard, Vasiliy Makhalov, Davide Dreon, Jean Dalibard, Leonid A. Sidorenkov, and Sylvain Nascimbene. Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom. Nature Communications, 9 (1), nov 2018. 10.1038\/s41467-018-07433-1. URL https:\/\/doi.org\/10.1038.","DOI":"10.1038\/s41467-018-07433-1"},{"key":"3","doi-asserted-by":"publisher","unstructured":"L. Chomaz, S. Baier, D. Petter, M. J. Mark, F. W\u00e4chtler, L. Santos, and F. Ferlaino. Quantum-fluctuation-driven crossover from a dilute bose-einstein condensate to a macrodroplet in a dipolar quantum fluid. Phys. Rev. X, 6: 041039, Nov 2016. 10.1103\/PhysRevX.6.041039. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevX.6.041039.","DOI":"10.1103\/PhysRevX.6.041039"},{"key":"4","doi-asserted-by":"publisher","unstructured":"Tommaso Comparin, Fabio Mezzacapo, and Tommaso Roscilde. Multipartite entangled states in dipolar quantum simulators. Physical Review Letters, 129 (15), oct 2022a. 10.1103\/physrevlett.129.150503. URL https:\/\/doi.org\/10.1103.","DOI":"10.1103\/physrevlett.129.150503"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Tommaso Comparin, Fabio Mezzacapo, and Tommaso Roscilde. Robust spin squeezing from the tower of states of u(1)-symmetric spin hamiltonians. Phys. Rev. A, 105: 022625, Feb 2022b. 10.1103\/PhysRevA.105.022625. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevA.105.022625.","DOI":"10.1103\/PhysRevA.105.022625"},{"key":"6","doi-asserted-by":"publisher","unstructured":"L.-M. Duan, J. I. Cirac, and P. Zoller. Quantum entanglement in spinor bose-einstein condensates. Phys. Rev. A, 65: 033619, Feb 2002. 10.1103\/PhysRevA.65.033619. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevA.65.033619.","DOI":"10.1103\/PhysRevA.65.033619"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Nils J. Engelsen, Rajiv Krishnakumar, Onur Hosten, and Mark A. Kasevich. Bell Correlations in Spin-Squeezed States of 500 000 Atoms. Phys. Rev. Lett., 118 (14): 140401, April 2017. 10.1103\/PhysRevLett.118.140401. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.118.140401.","DOI":"10.1103\/PhysRevLett.118.140401"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Bertrand Evrard, An Qu, Jean Dalibard, and Fabrice Gerbier. From many-body oscillations to thermalization in an isolated spinor gas. Phys. Rev. Lett., 126: 063401, Feb 2021a. 10.1103\/PhysRevLett.126.063401. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.126.063401.","DOI":"10.1103\/PhysRevLett.126.063401"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Bertrand Evrard, An Qu, Jean Dalibard, and Fabrice Gerbier. Observation of fragmentation of a spinor bose-einstein condensate. Science, 373 (6561): 1340\u20131343, 2021b. 10.1126\/science.abd8206. URL https:\/\/www.science.org\/doi\/abs\/10.1126\/science.abd8206.","DOI":"10.1126\/science.abd8206"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Ir\u00e9n\u00e9e Fr\u00e9rot and Tommaso Roscilde. Quantum critical metrology. Phys. Rev. Lett., 121: 020402, Jul 2018. 10.1103\/PhysRevLett.121.020402. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.121.020402.","DOI":"10.1103\/PhysRevLett.121.020402"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Ir\u00e9n\u00e9e Fr\u00e9rot, Flavio Baccari, and Antonio Ac\u00edn. Unveiling quantum entanglement in many-body systems from partial information. arXiv preprint arXiv:2107.03944, 2021. https:\/\/doi.org\/10.48550\/arXiv.2107.03944. URL https:\/\/arxiv.org\/abs\/2107.03944.","DOI":"10.48550\/arXiv.2107.03944"},{"key":"12","doi-asserted-by":"publisher","unstructured":"Albert Frisch, Michael Mark, Kiyotaka Aikawa, Francesca Ferlaino, John L. Bohn, Constantinos Makrides, Alexander Petrov, and Svetlana Kotochigova. Quantum chaos in ultracold collisions of gas-phase erbium atoms. Nature, 507 (7493): 475\u2013479, Mar 2014. ISSN 1476-4687. 10.1038\/nature13137. URL http:\/\/dx.doi.org\/10.1038\/nature13137.","DOI":"10.1038\/nature13137"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Lucas Gabardos, Bihui Zhu, Steven Lepoutre, Ana Maria Rey, Bruno Laburthe-Tolra, and Laurent Vernac. Relaxation of the collective magnetization of a dense 3d array of interacting dipolar $s=3$ atoms. Phys. Rev. Lett., 125: 143401, Sep 2020. 10.1103\/PhysRevLett.125.143401. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.125.143401.","DOI":"10.1103\/PhysRevLett.125.143401"},{"key":"14","doi-asserted-by":"publisher","unstructured":"I. M. Georgescu, S. Ashhab, and Franco Nori. Quantum simulation. Rev. Mod. Phys., 86: 153\u2013185, Mar 2014. 10.1103\/RevModPhys.86.153. URL https:\/\/link.aps.org\/doi\/10.1103\/RevModPhys.86.153.","DOI":"10.1103\/RevModPhys.86.153"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Manuel Gessner, Augusto Smerzi, and Luca Pezz\u00e8. Metrological nonlinear squeezing parameter. Phys. Rev. Lett., 122: 090503, Mar 2019. 10.1103\/PhysRevLett.122.090503. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.122.090503.","DOI":"10.1103\/PhysRevLett.122.090503"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Kevin A. Gilmore, Matthew Affolter, Robert J. Lewis-Swan, Diego Barberena, Elena Jordan, Ana Maria Rey, and John J. Bollinger. Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals. Science, 373 (6555): 673\u2013678, Aug 2021. ISSN 1095-9203. 10.1126\/science.abi5226. URL http:\/\/dx.doi.org\/10.1126\/science.abi5226.","DOI":"10.1126\/science.abi5226"},{"key":"17","doi-asserted-by":"publisher","unstructured":"C. D. Hamley, C. S. Gerving, T. M. Hoang, E. M. Bookjans, and M. S. Chapman. Spin-nematic squeezed vacuum in a quantum gas. Nature Physics, 8 (4): 305\u2013308, Feb 2012. ISSN 1745-2481. 10.1038\/nphys2245. URL http:\/\/dx.doi.org\/10.1038\/nphys2245.","DOI":"10.1038\/nphys2245"},{"key":"18","doi-asserted-by":"publisher","unstructured":"Holger Kadau, Matthias Schmitt, Matthias Wenzel, Clarissa Wink, Thomas Maier, Igor Ferrier-Barbut, and Tilman Pfau. Observing the rosensweig instability of a quantum ferrofluid. Nature, 530 (7589): 194\u2013197, Feb 2016. ISSN 1476-4687. 10.1038\/nature16485. URL http:\/\/dx.doi.org\/10.1038\/nature16485.","DOI":"10.1038\/nature16485"},{"key":"19","doi-asserted-by":"publisher","unstructured":"Valentin Kasper, Daniel Gonz\u00e1lez-Cuadra, Apoorva Hegde, Andy Xia, Alexandre Dauphin, Felix Huber, Eberhard Tiemann, Maciej Lewenstein, Fred Jendrzejewski, and Philipp Hauke. Universal quantum computation and quantum error correction with ultracold atomic mixtures. Quantum Science and Technology, 7 (1): 015008, 2021. 10.1088\/2058-9565\/ac2d39.","DOI":"10.1088\/2058-9565\/ac2d39"},{"key":"20","doi-asserted-by":"publisher","unstructured":"Yuki Kawaguchi and Masahito Ueda. Spinor bose\u2013einstein condensates. Physics Reports, 520 (5): 253\u2013381, 2012. ISSN 0370-1573. https:\/\/doi.org\/10.1016\/j.physrep.2012.07.005. URL https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0370157312002098. Spinor Bose\u2013Einstein condensates.","DOI":"10.1016\/j.physrep.2012.07.005"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Masahiro Kitagawa and Masahito Ueda. Squeezed spin states. Phys. Rev. A, 47: 5138\u20135143, Jun 1993. 10.1103\/PhysRevA.47.5138. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevA.47.5138.","DOI":"10.1103\/PhysRevA.47.5138"},{"key":"22","doi-asserted-by":"publisher","unstructured":"Jia Kong, Ricardo Jim\u00e9nez-Mart\u00ednez, Charikleia Troullinou, Vito Giovanni Lucivero, G\u00e9za T\u00f3th, and Morgan W. Mitchell. Measurement-induced, spatially-extended entanglement in a hot, strongly-interacting atomic system. Nature Communications, 11 (1), May 2020. ISSN 2041-1723. 10.1038\/s41467-020-15899-1. URL http:\/\/dx.doi.org\/10.1038\/s41467-020-15899-1.","DOI":"10.1038\/s41467-020-15899-1"},{"key":"23","doi-asserted-by":"publisher","unstructured":"Philipp Kunkel, Maximilian Pr\u00fcfer, Helmut Strobel, Daniel Linnemann, Anika Fr\u00f6lian, Thomas Gasenzer, Martin G\u00e4rttner, and Markus K. Oberthaler. Spatially distributed multipartite entanglement enables epr steering of atomic clouds. Science, 360 (6387): 413\u2013416, 2018. 10.1126\/science.aao2254. URL https:\/\/www.science.org\/doi\/abs\/10.1126\/science.aao2254.","DOI":"10.1126\/science.aao2254"},{"key":"24","doi-asserted-by":"publisher","unstructured":"Philipp Kunkel, Maximilian Pr\u00fcfer, Stefan Lannig, Rodrigo Rosa-Medina, Alexis Bonnin, Martin G\u00e4rttner, Helmut Strobel, and Markus K. Oberthaler. Simultaneous readout of noncommuting collective spin observables beyond the standard quantum limit. Phys. Rev. Lett., 123: 063603, Aug 2019. 10.1103\/PhysRevLett.123.063603. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.123.063603.","DOI":"10.1103\/PhysRevLett.123.063603"},{"key":"25","doi-asserted-by":"publisher","unstructured":"Karsten Lange, Jan Peise, Bernd L\u00fccke, Ilka Kruse, Giuseppe Vitagliano, Iagoba Apellaniz, Matthias Kleinmann, G\u00e9za T\u00f3th, and Carsten Klempt. Entanglement between two spatially separated atomic modes. Science, 360 (6387): 416\u2013418, 2018. 10.1126\/science.aao2035. URL https:\/\/www.science.org\/doi\/abs\/10.1126\/science.aao2035.","DOI":"10.1126\/science.aao2035"},{"key":"26","doi-asserted-by":"publisher","unstructured":"E. Lucioni, L. Tanzi, A. Fregosi, J. Catani, S. Gozzini, M. Inguscio, A. Fioretti, C. Gabbanini, and G. Modugno. Dysprosium dipolar bose-einstein condensate with broad feshbach resonances. Phys. Rev. A, 97: 060701, Jun 2018. 10.1103\/PhysRevA.97.060701. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevA.97.060701.","DOI":"10.1103\/PhysRevA.97.060701"},{"key":"27","doi-asserted-by":"publisher","unstructured":"Xin-Yu Luo, Yi-Quan Zou, Ling-Na Wu, Qi Liu, Ming-Fei Han, Meng Khoon Tey, and Li You. Deterministic entanglement generation from driving through quantum phase transitions. Science, 355 (6325): 620\u2013623, 2017. 10.1126\/science.aag1106. URL https:\/\/www.science.org\/doi\/abs\/10.1126\/science.aag1106.","DOI":"10.1126\/science.aag1106"},{"key":"28","doi-asserted-by":"publisher","unstructured":"Jian Ma, Xiaoguang Wang, C.P. Sun, and Franco Nori. Quantum spin squeezing. Physics Reports, 509 (2-3): 89\u2013165, dec 2011. 10.1016\/j.physrep.2011.08.003. URL https:\/\/doi.org\/10.1016.","DOI":"10.1016\/j.physrep.2011.08.003"},{"key":"29","doi-asserted-by":"publisher","unstructured":"Guillem M\u00fcller-Rigat, Albert Aloy, Maciej Lewenstein, and Ir\u00e9n\u00e9e Fr\u00e9rot. Inferring nonlinear many-body bell inequalities from average two-body correlations: Systematic approach for arbitrary spin-$j$ ensembles. PRX Quantum, 2: 030329, Aug 2021. 10.1103\/PRXQuantum.2.030329. URL https:\/\/link.aps.org\/doi\/10.1103\/PRXQuantum.2.030329.","DOI":"10.1103\/PRXQuantum.2.030329"},{"key":"30","doi-asserted-by":"publisher","unstructured":"Luca Pezz\u00e8, Augusto Smerzi, Markus K. Oberthaler, Roman Schmied, and Philipp Treutlein. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys., 90: 035005, Sep 2018. 10.1103\/RevModPhys.90.035005. URL https:\/\/link.aps.org\/doi\/10.1103\/RevModPhys.90.035005.","DOI":"10.1103\/RevModPhys.90.035005"},{"key":"31","doi-asserted-by":"publisher","unstructured":"Angelo Piga, Albert Aloy, Maciej Lewenstein, and Ir\u00e9n\u00e9e Fr\u00e9rot. Bell correlations at ising quantum critical points. Phys. Rev. Lett., 123: 170604, Oct 2019. 10.1103\/PhysRevLett.123.170604. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.123.170604.","DOI":"10.1103\/PhysRevLett.123.170604"},{"key":"32","doi-asserted-by":"publisher","unstructured":"An Qu, Bertrand Evrard, Jean Dalibard, and Fabrice Gerbier. Probing spin correlations in a bose-einstein condensate near the single-atom level. Phys. Rev. Lett., 125: 033401, Jul 2020. 10.1103\/PhysRevLett.125.033401. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.125.033401.","DOI":"10.1103\/PhysRevLett.125.033401"},{"key":"33","doi-asserted-by":"publisher","unstructured":"Martin Ringbauer, Michael Meth, Lukas Postler, Roman Stricker, Rainer Blatt, Philipp Schindler, and Thomas Monz. A universal qudit quantum processor with trapped ions. Nature Physics, 18 (9): 1053\u20131057, jul 2022. 10.1038\/s41567-022-01658-0. URL https:\/\/www.nature.com\/articles\/s41567-022-01658-0.","DOI":"10.1038\/s41567-022-01658-0"},{"key":"34","doi-asserted-by":"publisher","unstructured":"Roman Schmied, Jean-Daniel Bancal, Baptiste Allard, Matteo Fadel, Valerio Scarani, Philipp Treutlein, and Nicolas Sangouard. Bell correlations in a Bose-Einstein condensate. Science, 352 (6284): 441\u2013444, April 2016. ISSN 0036-8075, 1095-9203. 10.1126\/science.aad8665. URL http:\/\/science.sciencemag.org\/content\/352\/6284\/441.","DOI":"10.1126\/science.aad8665"},{"key":"35","doi-asserted-by":"publisher","unstructured":"A. S\u00f8rensen, L.-M. Duan, J. I. Cirac, and P. Zoller. Many-particle entanglement with bose\u2013einstein condensates. Nature, 409 (6816): 63\u201366, jan 2001. 10.1038\/35051038. URL https:\/\/doi.org\/10.1038.","DOI":"10.1038\/35051038"},{"key":"36","doi-asserted-by":"publisher","unstructured":"Anders S. S\u00f8rensen and Klaus M\u00f8lmer. Entanglement and extreme spin squeezing. Phys. Rev. Lett., 86: 4431\u20134434, May 2001a. 10.1103\/PhysRevLett.86.4431. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.86.4431.","DOI":"10.1103\/PhysRevLett.86.4431"},{"key":"37","doi-asserted-by":"publisher","unstructured":"Anders S. S\u00f8rensen and Klaus M\u00f8lmer. Entanglement and extreme spin squeezing. Phys. Rev. Lett., 86: 4431\u20134434, May 2001b. 10.1103\/PhysRevLett.86.4431. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.86.4431.","DOI":"10.1103\/PhysRevLett.86.4431"},{"key":"38","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, Apr 2009. 10.1103\/PhysRevA.79.042334. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevA.79.042334.","DOI":"10.1103\/PhysRevA.79.042334"},{"key":"39","doi-asserted-by":"publisher","unstructured":"A. Trautmann, P. Ilzh\u00f6fer, G. Durastante, C. Politi, M. Sohmen, M. J. Mark, and F. Ferlaino. Dipolar quantum mixtures of erbium and dysprosium atoms. Phys. Rev. Lett., 121: 213601, Nov 2018. 10.1103\/PhysRevLett.121.213601. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.121.213601.","DOI":"10.1103\/PhysRevLett.121.213601"},{"key":"40","doi-asserted-by":"publisher","unstructured":"Giuseppe Vitagliano, Philipp Hyllus, I\u00f1igo L. Egusquiza, and G\u00e9za T\u00f3th. Spin squeezing inequalities for arbitrary spin. Phys. Rev. Lett., 107: 240502, Dec 2011. 10.1103\/PhysRevLett.107.240502. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.107.240502.","DOI":"10.1103\/PhysRevLett.107.240502"},{"key":"41","doi-asserted-by":"publisher","unstructured":"Giuseppe Vitagliano, Iagoba Apellaniz, I\u00f1igo L. Egusquiza, and G\u00e9za T\u00f3th. Spin squeezing and entanglement for an arbitrary spin. Phys. Rev. A, 89: 032307, Mar 2014. 10.1103\/PhysRevA.89.032307. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevA.89.032307.","DOI":"10.1103\/PhysRevA.89.032307"},{"key":"42","doi-asserted-by":"publisher","unstructured":"Matthias Wenzel, Fabian B\u00f6ttcher, Jan-Niklas Schmidt, Michael Eisenmann, Tim Langen, Tilman Pfau, and Igor Ferrier-Barbut. Anisotropic superfluid behavior of a dipolar bose-einstein condensate. Physical Review Letters, 121 (3), Jul 2018. ISSN 1079-7114. 10.1103\/physrevlett.121.030401. URL http:\/\/dx.doi.org\/10.1103\/PhysRevLett.121.030401.","DOI":"10.1103\/physrevlett.121.030401"},{"key":"43","doi-asserted-by":"publisher","unstructured":"D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen. Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A, 50: 67\u201388, Jul 1994. 10.1103\/PhysRevA.50.67. URL https:\/\/link.aps.org\/doi\/10.1103\/PhysRevA.50.67.","DOI":"10.1103\/PhysRevA.50.67"},{"key":"44","doi-asserted-by":"publisher","unstructured":"Yi-Quan Zou, Ling-Na Wu, Qi Liu, Xin-Yu Luo, Shuai-Feng Guo, Jia-Hao Cao, Meng Khoon Tey, and Li You. Beating the classical precision limit with spin-1 dicke states of more than 10,000 atoms. Proceedings of the National Academy of Sciences, 115 (25): 6381\u20136385, Jun 2018. ISSN 1091-6490. 10.1073\/pnas.1715105115. URL http:\/\/dx.doi.org\/10.1073\/pnas.1715105115.","DOI":"10.1073\/pnas.1715105115"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-12-29-887\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T15:40:19Z","timestamp":1672328419000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-12-29-887\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,29]]},"references-count":45,"URL":"https:\/\/doi.org\/10.22331\/q-2022-12-29-887","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,29]]},"article-number":"887"}}