Eur. Phys. J. D (2014) 68: 347
https://doi.org/10.1140/epjd/e2014-50560-1

Regular Article

Bounds on quantum multiple-parameter estimation with Gaussian state

¹ Department of Physics, Xinyang Normal University, Xinyang, Henan 464000, P.R. China
² Hearne Institute for Theoretical Physics and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, 70803 LA, USA

^a e-mail: gaoyangchang@gmail.com

Received: 28 July 2014
Received in final form: 18 September 2014
Published online: 17 November 2014

Abstract

We investigate the quantum Cramer-Rao bounds on the joint multiple-parameter estimation with the Gaussian state as a probe. We derive the explicit right logarithmic derivative and symmetric logarithmic derivative operators in such a situation. We compute the corresponding quantum Fisher information matrices, and find that they can be fully expressed in terms of the mean displacement and covariance matrix of the Gaussian state. Finally, we give some examples to show the utility of our analytical results.