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Saturating quantum advantages in postselected metrology with the positive Kirkwood-Dirac distribution

Sourav Das1,2,*, Subhrajit Modak1,3,†, and Manabendra Nath Bera1,‡

  • 1Department of Physical Sciences, Indian Institute of Science Education and Research (IISER), Mohali, Punjab 140306, India
  • 2Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 3Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India

  • *sourav.iisermohali@gmail.com
  • †modoksuvrojit@gmail.com
  • ‡mnbera@gmail.com
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Phys. Rev. A 107, 042413 – Published 11 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042413

Abstract

Weak amplification and other postselection-based metrological protocols can enhance precision while estimating small parameters, outperforming postselection-free protocols. In general, these enhancements are largely constrained because the protocols yielding higher precision are rarely obtained due to a lower probability of successful postselection. It is shown that this precision can further be improved with the help of quantum resources like entanglement and negativity in the quasiprobability distribution. However, these quantum advantages in attaining considerable success probability with large precision are bounded irrespective of any accessible quantum resources. The advantage is being considered only within the scope of postselected metrology. Here we derive a bound of these advantages in postselected metrology, establishing a connection with weak value optimization where the latter can be understood in terms of the geometric phase. We introduce a scheme that saturates the bound, yielding anomalously large precision. Moreover, we prove that these advantages can be achieved with positive quasiprobability distribution. We also provide an optimal metrological scheme using a three-level nondegenerate quantum system.

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Comments & Replies

Comment on “Saturating quantum advantages in postselected metrology with the positive Kirkwood-Dirac distribution”

David R. M. Arvidsson-Shukur, Crispin H. W. Barnes, Hugo V. Lepage, Seth Lloyd, Noah Lupu-Gladstein, Wilfred Salmon, and Flavio Salvati
Phys. Rev. A 109, 066401 (2024)

Reply to “Comment on ‘Saturating quantum advantages in postselected metrology with the positive Kirkwood-Dirac distribution' ”

Sourav Das, Subhrajit Modak, and Manabendra Nath Bera
Phys. Rev. A 109, 066402 (2024)

Article Text

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Outline

Information

Phys. Rev. A 107, 042413– Published 11 April, 2023
  • Received 14 September 2021
  • Revised 18 September 2022
  • Accepted 20 March 2023
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