TR2022-048

Application of Pontryagin’s Maximum Principle to Quantum Metrology in Dissipative Systems


    •  Lin, C., Ma, Y., Sels, D., "Application of Pontryagin’s Maximum Principle to Quantum Metrology in Dissipative Systems", Physical Reivew A, May 2022.
      BibTeX TR2022-048 PDF
      • @article{Lin2022may,
      • author = {Lin, Chungwei and Ma, Yanting and Sels, Dries},
      • title = {Application of Pontryagin’s Maximum Principle to Quantum Metrology in Dissipative Systems},
      • journal = {Physical Reivew A},
      • year = 2022,
      • month = may,
      • url = {https://www.merl.com/publications/TR2022-048}
      • }
  • MERL Contacts:
  • Research Areas:

    Applied Physics, Control, Optimization

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 “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.

 

  • Related Publication

  •  Lin, C., Ma, Y., Sels, D., "Application of Pontryagin's Maximum Principle to Quantum Metrology in Dissipative Systems", arXiv, April 2022.
    BibTeX arXiv
    • @article{Lin2022apr,
    • author = {Lin, Chungwei and Ma, Yanting and Sels, Dries},
    • title = {Application of Pontryagin's Maximum Principle to Quantum Metrology in Dissipative Systems},
    • journal = {arXiv},
    • year = 2022,
    • month = apr,
    • url = {https://arxiv.org/abs/2205.00112}
    • }