Title: Sensitivity evolution in quantum Hamiltonian estimation

Authors: Yanjun Zhang; Lu Wang; Jun Zhang

Addresses: Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China; Key Laboratory of System Control and Information Processing (MOE), Shanghai Jiao Tong University, Shanghai, 200240, China ' Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China; Key Laboratory of System Control and Information Processing (MOE), Shanghai Jiao Tong University, Shanghai, 200240, China ' UMich-SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai, 200240, China; Key Laboratory of System Control and Information Processing (MOE), Shanghai Jiao Tong University, Shanghai, 200240, China

Abstract: In this paper we investigate the sensitivity evolution in estimating the unknown quantum Hamiltonian parameters. We apply Kullback-Liebler (KL) divergence to quantify the difference of quantum measurements between deviated and authentic parameter values. From explicit formula for the Fisher information matrix (FIM), we can calculate the second order approximation of the KL divergence. For several quantum mechanical systems, we use this analytical method to investigate the sensitivity evolution of estimating the underlying unknown parameters. We find that in all these examples the FIM is divergent, which indicates that it is possible to design an unbiased estimator that yields the unknown parameters precisely.

Keywords: parameter estimation; Fisher information matrix; FIM; sensitivity evolution.

DOI: 10.1504/IJSCC.2018.093402

International Journal of Systems, Control and Communications, 2018 Vol.9 No.3, pp.255 - 265

Received: 18 Oct 2017
Accepted: 27 Nov 2017

Published online: 01 Jun 2018 *

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