Quantum state estimation with nuisance parameters

Suzuki，Jun1; Yang，Yuxiang2; Hayashi，Masahito3,4,5,6

2020-11-01

10.1088/1751-8121/ab8b78

Journal of Physics A-Mathematical and Theoretical   影响因子和分区

1751-8113

1751-8121

In parameter estimation, nuisance parameters refer to parameters that are not of interest but nevertheless affect the precision of estimating other parameters of interest. For instance, the strength of noises in a probe can be regarded as a nuisance parameter. Despite its long history in classical statistics, the nuisance parameter problem in quantum estimation remains largely unexplored. The goal of this article is to provide a systematic review of quantum estimation in the presence of nuisance parameters, and to supply those who work in quantum tomography and quantum metrology with tools to tackle relevant problems. After an introduction to the nuisance parameter and quantum estimation theory, we explicitly formulate the problem of quantum state estimation with nuisance parameters. We extend quantum Cramér–Rao bounds to the nuisance parameter case and provide a parameter orthogonalization tool to separate the nuisance parameters from the parameters of interest. In particular, we put more focus on the case of one-parameter estimation in the presence of nuisance parameters, as it is most frequently encountered in practice.

Nuisance parameter Quantum Cramér–Rao bounds Quantum state estimation

SCI

英语

通讯

JSPS[17H01280][16KT0017][17K05571] ; Swiss National Science Foundation[200020_165843]

Physics

Physics, Multidisciplinary ; Physics, Mathematical

WOS:000582544700001

IOP PUBLISHING LTD

2-s2.0-85089968222

Scopus

1.Graduate School of Informatics and Engineering,University of Electro-Communications,Tokyo,182-8585,Japan
2.Institute for Theoretical Physics,ETH Zürich,Zürich,8093,Switzerland
3.Graduate School of Mathematics,Nagoya University,Nagoya,464-8602,Japan
4.Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China
5.Center for Quantum Computing,Peng Cheng Laboratory,Shenzhen,518000,China
6.Centre for Quantum Technologies,National University of Singapore,117542,Singapore

Suzuki，Jun,Yang，Yuxiang,Hayashi，Masahito. Quantum state estimation with nuisance parameters[J]. Journal of Physics A-Mathematical and Theoretical,2020,53(45).

Suzuki，Jun,Yang，Yuxiang,&Hayashi，Masahito.(2020).Quantum state estimation with nuisance parameters.Journal of Physics A-Mathematical and Theoretical,53(45).

Suzuki，Jun,et al."Quantum state estimation with nuisance parameters".Journal of Physics A-Mathematical and Theoretical 53.45(2020).