Optimal measurements for quantum multiparameter estimation with general states
Abstract
We generalize the approach by Braunstein and Caves, [Phys. Rev. Lett. 72, 3439 (1994)].PRLTAO0031-900710.1103/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 Cramér-Rao 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 Cramér-Rao 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 three-dimensional separation of two incoherent optical point sources.
- Authors:
-
[1];
- 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 Laboratory (FNAL), Batavia, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1569236
- Report Number(s):
- arXiv:1806.07337; FERMILAB-PUB-19-478-SCD
Journal ID: ISSN 2469-9926; PLRAAN; oai:inspirehep.net:1752865; TRN: US2100020
- Grant/Contract Number:
- AC02-07CH11359
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 3; Journal ID: ISSN 2469-9926
- 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. https://doi.org/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. https://doi.org/10.1103/PhysRevA.100.032104. https://www.osti.gov/servlets/purl/1569236.
@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)].PRLTAO0031-900710.1103/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 Cramér-Rao 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 Cramér-Rao 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 three-dimensional separation of two incoherent optical point sources.},
doi = {10.1103/PhysRevA.100.032104},
journal = {Physical Review A},
number = 3,
volume = 100,
place = {United States},
year = {Tue Sep 03 00:00:00 EDT 2019},
month = {Tue Sep 03 00:00:00 EDT 2019}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 41 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Entangling measurements for multiparameter estimation with two qubits
journal, November 2017
- Roccia, Emanuele; Gianani, Ilaria; Mancino, Luca
- Quantum Science and Technology, Vol. 3, Issue 1
Optical atomic clocks
journal, June 2015
- Ludlow, Andrew D.; Boyd, Martin M.; Ye, Jun
- Reviews of Modern Physics, Vol. 87, Issue 2
Explicit formula for the Holevo bound for two-parameter qubit-state estimation problem
journal, April 2016
- Suzuki, Jun
- Journal of Mathematical Physics, Vol. 57, Issue 4
Quantum Optical Technologies for Metrology, Sensing, and Imaging
journal, June 2015
- Dowling, Jonathan P.; Seshadreesan, Kaushik P.
- Journal of Lightwave Technology, Vol. 33, Issue 12
Modern description of Rayleigh's criterion
journal, January 2019
- Zhou, Sisi; Jiang, Liang
- Physical Review A, Vol. 99, Issue 1
Ultimate Precision Bound of Quantum and Subwavelength Imaging
journal, November 2016
- Lupo, Cosmo; Pirandola, Stefano
- Physical Review Letters, Vol. 117, Issue 19
Far-Field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit
journal, November 2016
- Nair, Ranjith; Tsang, Mankei
- Physical Review Letters, Vol. 117, Issue 19
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
journal, November 2004
- Giovannetti, V.
- Science, Vol. 306, Issue 5700
Advances in quantum metrology
journal, March 2011
- Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo
- Nature Photonics, Vol. 5, Issue 4
Spatial mode multiplexing/demultiplexing by Gouy phase interferometry
journal, December 2016
- Liñares, Jesús; Prieto-Blanco, Xesús; Montero-Orille, Carlos
- Optics Letters, Vol. 42, Issue 1
Discontinuities of the quantum Fisher information and the Bures metric
journal, May 2017
- Šafránek, Dominik
- Physical Review A, Vol. 95, Issue 5
Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases
journal, September 2017
- Pezzè, Luca; Ciampini, Mario A.; Spagnolo, Nicolò
- Physical Review Letters, Vol. 119, Issue 13
Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
journal, August 2016
- Tsang, Mankei; Nair, Ranjith; Lu, Xiao-Ming
- Physical Review X, Vol. 6, Issue 3
Principles of Optics
book, January 1999
- Born, Max; Wolf, Emil; Bhatia, A. B.
- Cambridge University Press
Quantum Limited Superresolution of an Incoherent Source Pair in Three Dimensions
journal, October 2018
- Yu, Zhixian; Prasad, Sudhakar
- Physical Review Letters, Vol. 121, Issue 18
Spin-Orbit-Coupled Interferometry with Ring-Trapped Bose-Einstein Condensates
journal, February 2018
- Helm, J. L.; Billam, T. P.; Rakonjac, A.
- Physical Review Letters, Vol. 120, Issue 6
Quantum Enhanced Estimation of a Multidimensional Field
journal, January 2016
- Baumgratz, Tillmann; Datta, Animesh
- Physical Review Letters, Vol. 116, Issue 3
Achieving the ultimate optical resolution
journal, January 2016
- Paúr, Martin; Stoklasa, Bohumil; Hradil, Zdenek
- Optica, Vol. 3, Issue 10
Colloquium : Physics of optical lattice clocks
journal, May 2011
- Derevianko, Andrei; Katori, Hidetoshi
- Reviews of Modern Physics, Vol. 83, Issue 2
Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode
journal, January 2016
- Yang, Fan; Tashchilina, Arina; Moiseev, E. S.
- Optica, Vol. 3, Issue 10
Interferometric space-mode multiplexing based on binary phase plates and refractive phase shifters
journal, January 2017
- Liñares, Jesús; Prieto-Blanco, Xesús; Moreno, Vicente
- Optics Express, Vol. 25, Issue 10
Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates
journal, September 2014
- Muessel, W.; Strobel, H.; Linnemann, D.
- Physical Review Letters, Vol. 113, Issue 10
Local Asymptotic Normality for Finite Dimensional Quantum Systems
journal, March 2009
- Kahn, Jonas; Guţă, Mădălin
- Communications in Mathematical Physics, Vol. 289, Issue 2
Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry
journal, June 2016
- Haine, Simon A.
- Physical Review Letters, Vol. 116, Issue 23
Multiple-parameter quantum estimation and measurement of nonselfadjoint observables
journal, November 1973
- Yuen, H.; Lax, M.
- IEEE Transactions on Information Theory, Vol. 19, Issue 6
The minimum variance of estimates in quantum signal detection
journal, March 1968
- Helstrom, C.
- IEEE Transactions on Information Theory, Vol. 14, Issue 2
Quantum Enhanced Multiple Phase Estimation
journal, August 2013
- Humphreys, Peter C.; Barbieri, Marco; Datta, Animesh
- Physical Review Letters, Vol. 111, Issue 7
Multi-parameter quantum metrology
journal, July 2016
- Szczykulska, Magdalena; Baumgratz, Tillmann; Datta, Animesh
- Advances in Physics: X, Vol. 1, Issue 4
Compatibility in multiparameter quantum metrology
journal, November 2016
- Ragy, Sammy; Jarzyna, Marcin; Demkowicz-Dobrzański, Rafał
- Physical Review A, Vol. 94, Issue 5
Optimal measurements for resolution beyond the Rayleigh limit
journal, January 2017
- Rehacek, J.; Paúr, M.; Stoklasa, B.
- Optics Letters, Vol. 42, Issue 2
Optimal estimation of joint parameters in phase space
journal, January 2013
- Genoni, M. G.; Paris, M. G. A.; Adesso, G.
- Physical Review A, Vol. 87, Issue 1
Optics and interferometry with atoms and molecules
journal, July 2009
- Cronin, Alexander D.; Schmiedmayer, Jörg; Pritchard, David E.
- Reviews of Modern Physics, Vol. 81, Issue 3
Sagnac Interferometry with a Single Atomic Clock
journal, October 2015
- Stevenson, R.; Hush, M. R.; Bishop, T.
- Physical Review Letters, Vol. 115, Issue 16
Quantum limit for two-dimensional resolution of two incoherent optical point sources
journal, June 2017
- Ang, Shan Zheng; Nair, Ranjith; Tsang, Mankei
- Physical Review A, Vol. 95, Issue 6
Real applications of quantum imaging
journal, June 2016
- Genovese, Marco
- Journal of Optics, Vol. 18, Issue 7
Fundamental Precision Bounds for Three-Dimensional Optical Localization Microscopy with Poisson Statistics
journal, July 2018
- Backlund, Mikael P.; Shechtman, Yoav; Walsworth, Ronald L.
- Physical Review Letters, Vol. 121, Issue 2
Quantum Estimation for Quantum Technology
journal, January 2009
- Paris, Matteo G. A.
- International Journal of Quantum Information, Vol. 07, Issue supp01
Quantum sensing
journal, July 2017
- Degen, C. L.; Reinhard, F.; Cappellaro, P.
- Reviews of Modern Physics, Vol. 89, Issue 3
Control-enhanced multiparameter quantum estimation
journal, October 2017
- Liu, Jing; Yuan, Haidong
- Physical Review A, Vol. 96, Issue 4
Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution
journal, December 2017
- Řehaček, J.; Hradil, Z.; Stoklasa, B.
- Physical Review A, Vol. 96, Issue 6
Probabilistic and Statistical Aspects of Quantum Theory
book, May 2011
- Holevo, Alexander
- Publications of the Scuola Normale Superiore
Sorting Photons by Radial Quantum Number
journal, December 2017
- Zhou, Yiyu; Mirhosseini, Mohammad; Fu, Dongzhi
- Physical Review Letters, Vol. 119, Issue 26
Sequential Feedback Scheme Outperforms the Parallel Scheme for Hamiltonian Parameter Estimation
journal, October 2016
- Yuan, Haidong
- Physical Review Letters, Vol. 117, Issue 16
A new approach to the Cramér-Rao-type bound of the pure-state model
journal, March 2002
- Matsumoto, K.
- Journal of Physics A: Mathematical and General, Vol. 35, Issue 13
Joint estimation of phase and phase diffusion for quantum metrology
journal, April 2014
- Vidrighin, Mihai D.; Donati, Gaia; Genoni, Marco G.
- Nature Communications, Vol. 5, Issue 1
Beating Rayleigh’s Curse by Imaging Using Phase Information
journal, February 2017
- Tham, Weng-Kian; Ferretti, Hugo; Steinberg, Aephraim M.
- Physical Review Letters, Vol. 118, Issue 7
Quantum imaging
journal, December 2005
- D'Angelo, M.; Shih, Y. H.
- Laser Physics Letters, Vol. 2, Issue 12
Quantum Limit for Two-Dimensional Resolution of Two Incoherent Optical Point Sources
conference, January 2016
- Ang, Shan Zheng; Nair, Ranjith; Tsang, Mankei
- CLEO: Applications and Technology, Conference on Lasers and Electro-Optics
Quantum Imaging
conference, January 2007
- Shih, Yanhua
- International Conference on Quantum Information
Optical atomic clocks
other, January 2015
- Ludlow, Andrew D.; Boyd, Martin M.; Ye, Jun
- College Park, MD : American Physical Society
Quantum Imaging
journal, January 2007
- Shih, Yanhua
- IEEE Journal of Selected Topics in Quantum Electronics, Vol. 13, Issue 4
Quantum Imaging
conference, August 2007
- Shih, Yanhua
- 2007 Conference on Lasers and Electro-Optics - Pacific Rim
Colloquium: Physics of optical lattice clocks
text, January 2010
- Derevianko, Andrei; Katori, Hidetoshi
- arXiv
Advances in Quantum Metrology
text, January 2011
- Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo
- arXiv
Gravitational Radiation Detection with Laser Interferometry
text, January 2013
- Adhikari, Rana X.
- arXiv
Quantum Enhanced Multiple Phase Estimation
text, January 2013
- Humphreys, Peter C.; Barbieri, Marco; Datta, Animesh
- arXiv
Explicit formula for the Holevo bound for two-parameter qubit estimation problem
text, January 2015
- Suzuki, Jun
- arXiv
Mean-field Dynamics and Fisher Information in matterwave Interferometry
text, January 2015
- Haine, Simon A.
- arXiv
Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation
text, January 2016
- Yuan, Haidong
- arXiv
Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit
text, January 2016
- Nair, Ranjith; Tsang, Mankei
- arXiv
Multi-parameter Quantum Metrology
text, January 2016
- Szczykulska, Magdalena; Baumgratz, Tillmann; Datta, Animesh
- arXiv
Discontinuities of the quantum Fisher information and the Bures metric
text, January 2016
- Šafránek, Dominik
- arXiv
Spin-orbit coupled interferometry with ring-trapped Bose--Einstein condensates
text, January 2017
- Helm, John L.; Billam, Thomas P.; Rakonjac, Ana
- arXiv
Optimal measurements for simultaneous quantum estimation of multiple phases
text, January 2017
- Pezzè, Luca; Ciampini, Mario A.; Spagnolo, Nicolò
- arXiv
Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution
text, January 2017
- Rehacek, J.; Hradil, Z.; Stoklasa, B.
- arXiv
Quantum-enhanced measurements: beating the standard quantum limit
text, January 2004
- Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo
- arXiv
A new approach to the Cramer-Rao type bound of the pure state model
text, January 1997
- matsumoto, Keiji
- arXiv
Works referencing / citing this record:
Quantum Fisher information matrix and multiparameter estimation
journal, December 2019
- Liu, Jing; Yuan, Haidong; Lu, Xiao-Ming
- Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 2
An upper bound on the number of compatible parameters in simultaneous quantum estimation
journal, February 2020
- Kukita, Shingo
- Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 9
Evaluating the Holevo Cramér-Rao Bound for Multiparameter Quantum Metrology
journal, November 2019
- Albarelli, Francesco; Friel, Jamie F.; Datta, Animesh
- Physical Review Letters, Vol. 123, Issue 20