Error estimation of different schemes to measure spin-squeezing inequalities

Year: 2024

Authors: Boensel JL., Imai S., Liu YC., G’hne O.

Autors Affiliation: Univ Siegen, Naturwissenschaftlich Tech Fak, Walter Flex Str 3, D-57068 Siegen, Germany; QSTAR, INO CNR & LENS, Largo Enr Fermi 2, I-50125 Florence, Italy.

Abstract: How can we analyze quantum correlations in large and noisy systems without quantum state tomography’ An established method is to measure total angular momenta and employ the so-called spin-squeezing inequalities based on their expectations and variances. This allows detection of metrologically useful entanglement, but efficient strategies for estimating such nonlinear quantities have yet to be determined. In this paper we show that spin-squeezing inequalities can not only be evaluated by measurements of the total angular momentum but also by two-qubit correlations, either involving all pair correlations or randomly chosen pair correlations. Then we analyze the estimation errors of our approaches in terms of a hypothesis test. For this purpose, we discuss how error bounds can be derived for nonlinear estimators with the help of their variances, characterizing the probability of falsely detecting a separable state as entangled. We focus on the spin-squeezing inequalities in multiqubit systems. Our methods, however, can also be applied to spin-squeezing inequalities for qudits or for the statistical treatment of other nonlinear parameters of quantum states.

Journal/Review: PHYSICAL REVIEW A

Volume: 110 (2)      Pages from: 22410-1  to: 22410-20

More Information: The authors would like to thank Kiara Hansenne, An-dreas Ketterer, Matthias Kleinmann, Martin Kliesch, Rene Schwonnek, Geza Toth, Lina Vandre, and Nikolai Wyderka for useful discussions and comments. This work has been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Projects No. 447948357 and No. 440958198) , the Sino-German Center for Research Promotion (Project No. M-0294) , and the German Ministry of Education and Research (Project QuKuK, BMBF Grant No. 16KIS1618K) . J.L.B. acknowledges support from the House of Young Talents of the University of Siegen. S.I. acknowledges support from the DAAD.
KeyWords: Entanglement; States
DOI: 10.1103/PhysRevA.110.022410

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