Optimal function estimation with photonic quantum sensor networks

Bringewatt, Jacob; Ehrenberg, Adam; Goel, Tarushii; Gorshkov, Alexey V.

doi:10.1103/PhysRevResearch.6.013246

Optimal function estimation with photonic quantum sensor networks

Journal Article · Wed Mar 06 00:00:00 EST 2024 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.6.013246· OSTI ID:2319044

Bringewatt, Jacob; ; Goel, Tarushii;

The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here we resolve a number of open questions that arise when extending this framework to Mach-Zehnder interferometers and quadrature displacement sensing. In particular, we derive lower bounds on the achievable mean square error in estimating a linear function of either local phase shifts or quadrature displacements. In the case of local phase shifts, these results prove, and somewhat generalize, a conjecture by Proctor []. For quadrature displacements, we extend proofs of lower bounds to the case of arbitrary linear functions. We provide optimal protocols achieving these bounds up to small (multiplicative) constants and describe an algebraic approach to deriving new optimal protocols, possibly subject to additional constraints. Using this approach, we prove necessary conditions for the amount of entanglement needed for any optimal protocol for both local phase and displacement sensing. Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0020312; SC0019040; SC0024220

OSTI ID:: 2319044

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Vol. 6 Journal Issue: 1; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (40)

Generalized Limits for Single-Parameter Quantum Estimation Boixo, Sergio; Flammia, Steven T.; Caves, Carlton M. Physical Review Letters, Vol. 98, Issue 9 https://doi.org/10.1103/PhysRevLett.98.090401	journal	February 2007
Distributed Quantum Metrology with Linear Networks and Separable Inputs Ge, Wenchao; Jacobs, Kurt; Eldredge, Zachary Physical Review Letters, Vol. 121, Issue 4 https://doi.org/10.1103/PhysRevLett.121.043604	journal	July 2018
Demonstration of a Reconfigurable Entangled Radio-Frequency Photonic Sensor Network Xia, Yi; Li, Wei; Clark, William Physical Review Letters, Vol. 124, Issue 15 https://doi.org/10.1103/PhysRevLett.124.150502	journal	April 2020
Optimal distributed quantum sensing using Gaussian states Oh, Changhun; Lee, Changhyoup; Lie, Seok Hyung Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023030	journal	April 2020
Multiparameter Estimation in Networked Quantum Sensors Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A. Physical Review Letters, Vol. 120, Issue 8 https://doi.org/10.1103/PhysRevLett.120.080501	journal	February 2018
Optimal measurement of field properties with quantum sensor networks Qian, Timothy; Bringewatt, Jacob; Boettcher, Igor Physical Review A, Vol. 103, Issue 3 https://doi.org/10.1103/PhysRevA.103.L030601	journal	March 2021
Quantum Metrology Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo Physical Review Letters, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevLett.96.010401	journal	January 2006
Achieving Heisenberg scaling with maximally entangled states: An analytic upper bound for the attainable root-mean-square error Belliardo, Federico; Giovannetti, Vittorio Physical Review A, Vol. 102, Issue 4 https://doi.org/10.1103/PhysRevA.102.042613	journal	October 2020
Quantum state estimation with nuisance parameters Suzuki, Jun; Yang, Yuxiang; Hayashi, Masahito Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 45 https://doi.org/10.1088/1751-8121/ab8b78	journal	October 2020
Quantum sensing networks for the estimation of linear functions Rubio, Jesús; Knott, Paul A.; Proctor, Timothy J. Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 34 https://doi.org/10.1088/1751-8121/ab9d46	journal	August 2020
Heisenberg scaling precision in the estimation of functions of parameters in linear optical networks Triggiani, Danilo; Facchi, Paolo; Tamma, Vincenzo Physical Review A, Vol. 104, Issue 6 https://doi.org/10.1103/PhysRevA.104.062603	journal	December 2021
Quantum metrology with nonclassical states of atomic ensembles Pezzè, Luca; Smerzi, Augusto; Oberthaler, Markus K. Reviews of Modern Physics, Vol. 90, Issue 3 https://doi.org/10.1103/RevModPhys.90.035005	journal	September 2018
Robust calibration of a universal single-qubit gate set via robust phase estimation Kimmel, Shelby; Low, Guang Hao; Yoder, Theodore J. Physical Review A, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevA.92.062315	journal	December 2015
Robustness of asymmetry and coherence of quantum states Piani, Marco; Cianciaruso, Marco; Bromley, Thomas R. Physical Review A, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevA.93.042107	journal	April 2016
One from many: Estimating a function of many parameters Gross, Jonathan Arthur; Caves, Carlton M. Journal of Physics A: Mathematical and Theoretical https://doi.org/10.1088/1751-8121/abb9ed	journal	September 2020
Quantum Fisher information matrix and multiparameter estimation Liu, Jing; Yuan, Haidong; Lu, Xiao-Ming Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 2 https://doi.org/10.1088/1751-8121/ab5d4d	journal	December 2019
Protocols for estimating multiple functions with quantum sensor networks: Geometry and performance Bringewatt, Jacob; Boettcher, Igor; Niroula, Pradeep Physical Review Research, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevResearch.3.033011	journal	July 2021
Unifying Quantum and Classical Speed Limits on Observables García-Pintos, Luis Pedro; Nicholson, Schuyler B.; Green, Jason R. Physical Review X, Vol. 12, Issue 1 https://doi.org/10.1103/PhysRevX.12.011038	journal	February 2022
Minimum-entanglement protocols for function estimation Ehrenberg, Adam; Bringewatt, Jacob; Gorshkov, Alexey V. Physical Review Research, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevResearch.5.033228	journal	September 2023
Quantum Speed Limit for Physical Processes Taddei, M. M.; Escher, B. M.; Davidovich, L. Physical Review Letters, Vol. 110, Issue 5 https://doi.org/10.1103/PhysRevLett.110.050402	journal	January 2013
Field Demonstration of Distributed Quantum Sensing without Post-Selection Zhao, Si-Ran; Zhang, Yu-Zhe; Liu, Wen-Zhao Physical Review X, Vol. 11, Issue 3 https://doi.org/10.1103/PhysRevX.11.031009	journal	July 2021
Distributed quantum sensing in a continuous-variable entangled network Guo, Xueshi; Breum, Casper R.; Borregaard, Johannes Nature Physics https://doi.org/10.1038/s41567-019-0743-x	journal	December 2019
Optimal and secure measurement protocols for quantum sensor networks Eldredge, Zachary; Foss-Feig, Michael; Gross, Jonathan A. Physical Review A, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevA.97.042337	journal	April 2018
Parity measurements in quantum optical metrology Chiruvelli, Aravind; Lee, Hwang Journal of Modern Optics, Vol. 58, Issue 11 https://doi.org/10.1080/09500340.2011.585251	journal	June 2011
Distributed quantum phase estimation with entangled photons Liu, Li-Zheng; Zhang, Yu-Zhe; Li, Zheng-Da Nature Photonics, Vol. 15, Issue 2 https://doi.org/10.1038/s41566-020-00718-2	journal	November 2020
Distributed quantum sensing Zhang, Zheshen; Zhuang, Quntao Quantum Science and Technology, Vol. 6, Issue 4 https://doi.org/10.1088/2058-9565/abd4c3	journal	July 2021
Repeater-enhanced distributed quantum sensing based on continuous-variable multipartite entanglement Xia, Yi; Zhuang, Quntao; Clark, William Physical Review A, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevA.99.012328	journal	January 2019
Distributed quantum sensing with squeezed-vacuum light in a configurable array of Mach-Zehnder interferometers Malitesta, Marco; Smerzi, Augusto; Pezzè, Luca Physical Review A, Vol. 108, Issue 3 https://doi.org/10.1103/PhysRevA.108.032621	journal	September 2023
Distributed quantum phase sensing for arbitrary positive and negative weights Oh, Changhun; Jiang, Liang; Lee, Changhyoup Physical Review Research, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevResearch.4.023164	journal	May 2022
Approximate decoherence free subspaces for distributed sensing Hamann, Arne; Sekatski, Pavel; Dür, Wolfgang Quantum Science and Technology, Vol. 7, Issue 2 https://doi.org/10.1088/2058-9565/ac44de	journal	January 2022
Bayesian multiparameter quantum metrology with limited data Rubio, Jesús; Dunningham, Jacob Physical Review A, Vol. 101, Issue 3 https://doi.org/10.1103/PhysRevA.101.032114	journal	March 2020
Photonic quantum metrology Polino, Emanuele; Valeri, Mauro; Spagnolo, Nicolò AVS Quantum Science, Vol. 2, Issue 2 https://doi.org/10.1116/5.0007577	journal	June 2020
Resolving unattainable Cramer–Rao bounds for quantum sensors Hayashi, Masahito; Vinjanampathy, Sai; Kwek, L. C. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 52, Issue 1 https://doi.org/10.1088/1361-6455/aaf348	journal	December 2018
Distributed quantum sensing using continuous-variable multipartite entanglement Zhuang, Quntao; Zhang, Zheshen; Shapiro, Jeffrey H. Physical Review A, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevA.97.032329	journal	March 2018
π -Corrected Heisenberg Limit Górecki, Wojciech; Demkowicz-Dobrzański, Rafał; Wiseman, Howard M. Physical Review Letters, Vol. 124, Issue 3 https://doi.org/10.1103/PhysRevLett.124.030501	journal	January 2020
Attaining the Ultimate Precision Limit in Quantum State Estimation Yang, Yuxiang; Chiribella, Giulio; Hayashi, Masahito Communications in Mathematical Physics, Vol. 368, Issue 1 https://doi.org/10.1007/s00220-019-03433-4	journal	April 2019
Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control Deffner, Sebastian; Campbell, Steve Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 45 https://doi.org/10.1088/1751-8121/aa86c6	journal	October 2017
Heisenberg-scaling measurement protocol for analytic functions with quantum sensor networks Qian, Kevin; Eldredge, Zachary; Ge, Wenchao Physical Review A, Vol. 100, Issue 4 https://doi.org/10.1103/PhysRevA.100.042304	journal	October 2019
Computational Complexity Arora, Sanjeev; Barak, Boaz https://doi.org/10.1017/CBO9780511804090	journal	January 2009
Erratum: Robust calibration of a universal single-qubit gate set via robust phase estimation [Phys. Rev. A 92 , 062315 (2015)] Kimmel, Shelby; Low, Guang Hao; Yoder, Theodore J. Physical Review A, Vol. 104, Issue 6 https://doi.org/10.1103/PhysRevA.104.069901	journal	December 2021

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