Multiparameter Estimation in Networked Quantum Sensors
We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Sandia National Lab. (SNLCA), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States)
 Univ. of Nottingham (United Kingdom); Univ. of Sussex, Brighton (United Kingdom)
 Univ. of Sussex, Brighton (United Kingdom)
 Publication Date:
 Report Number(s):
 SAND201713642J
Journal ID: ISSN 00319007; PRLTAO; 659588; TRN: US1802617
 Grant/Contract Number:
 AC0494AL85000; NA0003525
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review Letters
 Additional Journal Information:
 Journal Volume: 120; Journal Issue: 8; Journal ID: ISSN 00319007
 Publisher:
 American Physical Society (APS)
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
 OSTI Identifier:
 1429719
 Alternate Identifier(s):
 OSTI ID: 1422465
Proctor, Timothy J., Knott, Paul A., and Dunningham, Jacob A.. Multiparameter Estimation in Networked Quantum Sensors. United States: N. p.,
Web. doi:10.1103/PhysRevLett.120.080501.
Proctor, Timothy J., Knott, Paul A., & Dunningham, Jacob A.. Multiparameter Estimation in Networked Quantum Sensors. United States. doi:10.1103/PhysRevLett.120.080501.
Proctor, Timothy J., Knott, Paul A., and Dunningham, Jacob A.. 2018.
"Multiparameter Estimation in Networked Quantum Sensors". United States.
doi:10.1103/PhysRevLett.120.080501.
@article{osti_1429719,
title = {Multiparameter Estimation in Networked Quantum Sensors},
author = {Proctor, Timothy J. and Knott, Paul A. and Dunningham, Jacob A.},
abstractNote = {We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.},
doi = {10.1103/PhysRevLett.120.080501},
journal = {Physical Review Letters},
number = 8,
volume = 120,
place = {United States},
year = {2018},
month = {2}
}