Application of Pontryagin's maximum principle to quantum metrology in dissipative systems

Chungwei Lin, Yanting Ma, and Dries Sels
Phys. Rev. A 105, 042621 – Published 29 April 2022

Abstract

Optimal control theory, also known as Pontryagin's maximum principle, is applied to the quantum parameter estimation in the presence of decoherence. An efficient procedure is devised to compute the gradient of quantum Fisher information with respect to the control parameters and is used to construct the optimal control protocol. The proposed procedure keeps the control problem in the time-invariant form so that both first-order and second-order optimality conditions derived from Pontryagin's maximum principle apply; the second-order condition turns out to be crucial when the optimal control contains singular arcs. Concretely we look for the optimal control that maximizes quantum Fisher information for the “twist and turn” problem. We find that the optimal control is singular without dissipation but can become unbounded once the quantum decoherence is introduced. An amplitude constraint is needed to guarantee a bounded solution. With quantum decoherence, the maximum quantum Fisher information happens at a finite time due to the decoherence, and the asymptotic value depends on the specific decoherence channel and the control of consideration.

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  • Received 2 December 2021
  • Revised 7 April 2022
  • Accepted 12 April 2022

DOI:https://doi.org/10.1103/PhysRevA.105.042621

©2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Chungwei Lin* and Yanting Ma

  • Mitsubishi Electric Research Laboratories, 201 Broadway, Cambridge, Massachusetts 02139, USA

Dries Sels

  • Department of physics, New York University, New York City, New York 10003, USA and Center for Computational Quantum Physics, Flatiron Institute, 162 5th Ave, New York, New York 10010, USA

  • *clin@merl.com

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Issue

Vol. 105, Iss. 4 — April 2022

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