Phase-space geometry and optimal state preparation in quantum metrology with collective spins

Muñoz-Arias, Manuel H. and Deutsch, Ivan H. and Poggi, Pablo M. (2023) Phase-space geometry and optimal state preparation in quantum metrology with collective spins. PRX Quantum, 4 (2). 020314. ISSN 2691-3399 (https://doi.org/10.1103/PRXQuantum.4.020314)

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Abstract

We revisit well-known protocols in quantum metrology using collective spins and propose a unifying picture for optimal state preparation based on a semiclassical description in phase space. We show how this framework allows for quantitative predictions of the timescales required to prepare various metrologically useful states, and that these predictions remain accurate even for moderate system sizes, surprisingly far from the classical limit. Furthermore, this framework allows us to build a geometric picture that relates optimal (exponentially fast) entangled probe preparation to the existence of separatrices connecting saddle points in phase space. We illustrate our results with the paradigmatic examples of the two-axis countertwisting and twisting-and-turning Hamiltonians, where we provide analytical expressions for all the relevant optimal timescales. Finally, we propose a generalization of these models to include p-body collective interaction (or p-order twisting), beyond the usual case of p=2. Using our geometric framework, we prove a no-go theorem for the local optimality of these models for p>2.

  • Item type:Article
    ID code:85810
    Dates:
    Date
    Event
    25 April 2023
    Published
    28 March 2023
    Accepted
    8 November 2022
    Submitted
    Notes:Funding Information: The authors are grateful to Tyler J. Volkoff and Jason Twamley for engaging discussions. This work is supported by NSF Grant No. PHY-1606989 and the Quantum Leap Challenge Institutes program (Grant No. 2016244). This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator (QSA). In the last stages of the manuscript conception, M.H.M.-A. was supported in part via funding from NSERC, the Canada First Research Excellence Fund, and the Ministère de l’Économie et de l’Innovation du Québec. Publisher Copyright: © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
    Subjects:Science > Physics > Optics. Light
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:15 Jun 2023 12:33
    Last modified:27 Apr 2024 00:36
    URI:https://strathprints.strath.ac.uk/id/eprint/85810
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