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First, we derive an uncertainty relation that plays the role of a number-phase uncertainty for spin systems. It is important that the relation is given with well-defined and easily measurable quantities, and that it does not need assuming infinite dimensional systems. Based on this uncertainty relation, we show how to detect bipartite entanglement in an unpolarized Dicke state of many spin-1\/2 particles. The particles are split into two subensembles, then collective angular momentum measurements are carried out locally on the two parts. First, we present a bipartite Einstein-Podolsky-Rosen (EPR) steering criterion. Then, we present an entanglement condition that can detect bipartite entanglement in such systems. We demonstrate the utility of the criteria by applying them to a recent experiment given in K. Lange et al. [Science 360, 416 (2018)] realizing a Dicke state in a Bose-Einstein condensate of cold atoms, in which the two subensembles were spatially separated from each other. Our methods also work well if split spin-squeezed states are considered. We show in a comprehensive way how to handle experimental imperfections, such as the nonzero particle number variance including the partition noise, and the fact that, while ideally BECs occupy a single spatial mode, in practice the population of other spatial modes cannot be fully suppressed.<\/jats:p>","DOI":"10.22331\/q-2023-02-09-914","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T12:35:41Z","timestamp":1675946141000},"page":"914","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles"],"prefix":"10.22331","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5563-3222","authenticated-orcid":false,"given":"Giuseppe","family":"Vitagliano","sequence":"first","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, AT-1090 Vienna, Austria"},{"name":"Theoretical Physics, University of the Basque Country UPV\/EHU, ES-48080 Bilbao, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3653-0030","authenticated-orcid":false,"given":"Matteo","family":"Fadel","sequence":"additional","affiliation":[{"name":"Department of Physics, ETH Z\u00fcrich, CH-8093 Z\u00fcrich, Switzerland"},{"name":"Department of Physics, University of Basel, CH-4056 Basel, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3688-3242","authenticated-orcid":false,"given":"Iagoba","family":"Apellaniz","sequence":"additional","affiliation":[{"name":"Theoretical Physics, University of the Basque Country UPV\/EHU, ES-48080 Bilbao, Spain"},{"name":"EHU Quantum Center, University of the Basque Country UPV\/EHU, Barrio Sarriena s\/n, ES-48940 Leioa, Biscay, Spain"},{"name":"Mechanical and Industrial Manufacturing Department, Mondragon Unibertsitatea, ES-20500 Mondrag\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5782-804X","authenticated-orcid":false,"given":"Matthias","family":"Kleinmann","sequence":"additional","affiliation":[{"name":"Naturwissenschaftlich-Technische Fakult\u00e4t, Universit\u00e4t Siegen, DE-57068 Siegen, Germany"},{"name":"Theoretical Physics, University of the Basque Country UPV\/EHU, ES-48080 Bilbao, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4883-8756","authenticated-orcid":false,"given":"Bernd","family":"L\u00fccke","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Quantenoptik, Leibniz Universit\u00e4t Hannover, DE-30167 Hannover, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2402-3162","authenticated-orcid":false,"given":"Carsten","family":"Klempt","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Quantenoptik, Leibniz Universit\u00e4t Hannover, DE-30167 Hannover, Germany"},{"name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e.V. 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