TY - JOUR

T1 - Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles

AU - Vitagliano, Giuseppe

AU - Fadel, Matteo

AU - Apellaniz, Iagoba

AU - Kleinmann, Matthias

AU - Lücke, Bernd

AU - Klempt, Carsten

AU - Tóth, Géza

N1 - Funding Information: We thank G. Colangelo, O. Gühne, P. Hyllus, M. W. Mitchell, and J. Peise for discussions. We acknowledge the support of the EU (COST Action CA15220, QuantERA CEBBEC, QuantERA MENTA, QuantERA QuSiED), the Spanish MCIU (Grant No. PCI2018-092896. No. PCI2022-132947), the Spanish Ministry of Science, Innovation and Universities and the European Regional Development Fund FEDER through Grant No. PGC2018-101355-B-I00 (MCIU/AEI/FEDER, EU) and through Grant No. PID2021-126273NB-I00 funded by MCIN/AEI/10.13039/501100011033 and by ”ERDF A way of making Europe”, the Basque Government (Grant No. IT986-16, No. IT1470-22), and the National Research, Development and Innovation Office NKFIH (Grant No. K124351, No. KH129601, No. 2019-2.1.7-ERA-NET-2020-00003). We thank the ”Frontline” Research Excellence Programme of the NKFIH (Grant No. KKP133827). We thank Project no. TKP2021-NVA-04, which has been implemented with the support provided by the Ministry of Innovation and Technology of Hungary from the National Research, Development and Innovation Fund, financed under the TKP2021-NVA funding scheme. We thank the Quantum Information National Laboratory of Hungary. G.T. is thankful for a Bessel Research Award from the Humboldt Foundation. The work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2123 QuantumFrontiers 390837967), and through CRC 1227 (DQ-mat), projects A02 and B01. M. F. was partially supported by the Research Fund of the University of Basel for Excellent Junior Researchers. We also thank the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Project No. 447948357), the ERC (Consolidator Grant 683107/TempoQ). G. V. acknowledges support from the Austrian Science Fund (FWF) through projects ZK 3 (Zukunftskolleg), M 2462-N27 (Lise-Meitner), and P 35810-N (Stand-Alone).

PY - 2023/2/9

Y1 - 2023/2/9

N2 - We present a method to detect bipartite entanglement based on number-phase-like uncertainty relations in split spin ensembles. 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.

AB - We present a method to detect bipartite entanglement based on number-phase-like uncertainty relations in split spin ensembles. 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.

KW - quant-ph

UR - http://www.scopus.com/inward/record.url?scp=85174255332&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2104.05663

DO - 10.48550/arXiv.2104.05663

M3 - Article

VL - 7

SP - 914

JO - Quantum

JF - Quantum

SN - 2521-327X

ER -