Optimal measurements for quantum multiparameter estimation with general states
Abstract
We generalize the approach by Braunstein and Caves, [Phys. Rev. Lett. 72, 3439 (1994)].PRLTAO0031900710.1103/PhysRevLett.72.3439 to quantum multiparameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement operator. The saturation of all these bounds results in the saturation of the matrix Helstrom CramérRao bound. Remarkably, the saturation of the matrix bound is equivalent to the saturation of the scalar bound with respect to any given positive definite weight matrix. Necessary and sufficient conditions are obtained for the optimal measurements that give rise to the Helstrom CramérRao bound associated with a general quantum state. To saturate the Helstrom bound with separable measurements or collective measurement entangling only a small number of identical states, we find it is necessary for the symmetric logarithmic derivatives to commute on the support of the state. As an important application of our results, we construct several local optimal measurements for the problem of estimating the threedimensional separation of two incoherent optical point sources.
 Authors:

 Univ. of Rochester, NY (United States)
 Univ. of Rochester, NY (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Univ. of Rochester, NY (United States); Chapman Univ., Orange, CA (United States)
 Publication Date:
 Research Org.:
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 OSTI Identifier:
 1569236
 Report Number(s):
 arXiv:1806.07337; FERMILABPUB19478SCD
Journal ID: ISSN 24699926; PLRAAN; oai:inspirehep.net:1752865
 Grant/Contract Number:
 AC0207CH11359
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review A
 Additional Journal Information:
 Journal Volume: 100; Journal Issue: 3; Journal ID: ISSN 24699926
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Yang, Jing, Pang, Shengshi, Zhou, Yiyu, and Jordan, Andrew N. Optimal measurements for quantum multiparameter estimation with general states. United States: N. p., 2019.
Web. doi:10.1103/PhysRevA.100.032104.
Yang, Jing, Pang, Shengshi, Zhou, Yiyu, & Jordan, Andrew N. Optimal measurements for quantum multiparameter estimation with general states. United States. doi:10.1103/PhysRevA.100.032104.
Yang, Jing, Pang, Shengshi, Zhou, Yiyu, and Jordan, Andrew N. Tue .
"Optimal measurements for quantum multiparameter estimation with general states". United States. doi:10.1103/PhysRevA.100.032104.
@article{osti_1569236,
title = {Optimal measurements for quantum multiparameter estimation with general states},
author = {Yang, Jing and Pang, Shengshi and Zhou, Yiyu and Jordan, Andrew N.},
abstractNote = {We generalize the approach by Braunstein and Caves, [Phys. Rev. Lett. 72, 3439 (1994)].PRLTAO0031900710.1103/PhysRevLett.72.3439 to quantum multiparameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement operator. The saturation of all these bounds results in the saturation of the matrix Helstrom CramérRao bound. Remarkably, the saturation of the matrix bound is equivalent to the saturation of the scalar bound with respect to any given positive definite weight matrix. Necessary and sufficient conditions are obtained for the optimal measurements that give rise to the Helstrom CramérRao bound associated with a general quantum state. To saturate the Helstrom bound with separable measurements or collective measurement entangling only a small number of identical states, we find it is necessary for the symmetric logarithmic derivatives to commute on the support of the state. As an important application of our results, we construct several local optimal measurements for the problem of estimating the threedimensional separation of two incoherent optical point sources.},
doi = {10.1103/PhysRevA.100.032104},
journal = {Physical Review A},
issn = {24699926},
number = 3,
volume = 100,
place = {United States},
year = {2019},
month = {9}
}