Estimating Hamiltonian fluctuations from quantum time averages

Navneet Sharma; Kumar Gautam; Harish Parthasarathy

Estimating Hamiltonian fluctuations from quantum time averages

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Author(s): Navneet Sharma¹ ; Kumar Gautam² ; Harish Parthasarathy³
- Affiliations: 1: Department of Electronics and Communication Engineering , Thapar Institute of Engineering and Technology Patiala , Punjab , India ;
  2: Quantum Research and Centre of Excellence QRACE , New Delhi , India ;
  3: Department of Electronics and Communication Engineering , Netaji Subhas University of Technology New Delhi , New Delhi , India
Source: Volume 1, Issue 2, December 2020, p. 62 – 71
DOI: 10.1049/iet-qtc.2020.0001 , Online ISSN 2632-8925

This is an open access article published by the IET under the Creative Commons Attribution-NonCommercial-NoDerivs License (http://creativecommons.org/licenses/by-nc-nd/3.0/)

Received 05/01/2020, Accepted 07/10/2020, Revised 07/10/2020, Published 13/10/2020

This study presents a framework for the enhancement of parameter estimation issues by computing the time average of several quantum observables measured under the evolution of the Hamiltonian system. These time-cum-quantum averages are expressed as a quadratic function of the orthogonal projections on the eigen subspaces of the system. Estimation of the parameters is done using the approximate time-independent perturbation theory assuming the other parameters to be small with respect to one of the parameters that is normalised to unity in the presence of noise. The study also proves that the derived expression for the mean square parameter estimation error attains the quantum limit. When the measurement noise is classical and for general positive operator-valued measure successive time, the authors derive an expression for the quantum Cramèr–Rao lower bound.

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