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

authored by: Giuseppe Vitagliano, Matteo Fadel, Iagoba Apellaniz, Matthias Kleinmann, Bernd Lücke, Carsten Klempt, Géza Tóth
Abstract: 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.
Organisation(s): Institute of Quantum Optics
External Organisation(s): Austrian Academy of Sciences
University of the Basque Country
ETH Zurich
University of Basel
Mondragon University
University of Siegen
German Aerospace Center (DLR)
Donostia International Physics Center (DIPC)
Ikerbasque, the Basque Foundation for Science
Hungarian Academy of Sciences
Type: Article
Journal: Quantum
Volume: 7
Pages: 914
ISSN: 2521-327X
Publication date: 09.02.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Atomic and Molecular Physics, and Optics, Physics and Astronomy (miscellaneous)
Electronic version(s): https://doi.org/10.48550/arXiv.2104.05663 (Access: Open)
https://doi.org/10.22331/q-2023-02-09-914 (Access: Open)

BibTeX

@article{2af85b3d644f417681ae65452f314dbd,
title = "Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles",
abstract = "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.",
keywords = "quant-ph",
author = "Giuseppe Vitagliano and Matteo Fadel and Iagoba Apellaniz and Matthias Kleinmann and Bernd L{\"u}cke and Carsten Klempt and G{\'e}za T{\'o}th",
note = "Funding Information: We thank G. Colangelo, O. G{\"u}hne, 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{\textquoteright}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). ",
year = "2023",
month = feb,
day = "9",
doi = "10.48550/arXiv.2104.05663",
language = "English",
volume = "7",
pages = "914",
journal = "Quantum",
issn = "2521-327X",
publisher = "Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften",
}