Exact quantum Fisher matrix results for distributed phases using multiphoton polarization Greenberger-Horne-Zeilinger states

Wang, Jiaxuan; Agarwal, Girish S.

doi:10.1103/physreva.111.012414

Exact quantum Fisher matrix results for distributed phases using multiphoton polarization Greenberger-Horne-Zeilinger states

Journal Article · Wed Jan 08 00:00:00 EST 2025 · Physical Review A

DOI:https://doi.org/10.1103/physreva.111.012414· OSTI ID:2497739

^[1]; ^[1]

Texas A&M University, College Station, TX (United States)

Recently, distributed sensing has been extensively studied using squeezed states. While this is an excellent development, it is desirable to investigate the use of other quantum probes, such as entangled states of light. In this paper, we focus on distributed sensing, i.e., estimating multiple unknown phases at different spatial nodes using multiphoton polarization-entangled Greenberger-Horne-Zeilinger states distributed across different nodes. We utilize tools of quantum metrology and calculate the quantum Fisher information matrix (QFIM). However, the QFIM turns out to be singular, hindering the determination of quantum Cramér-Rao bounds for the parameters of interest. Recent experiments have contended with a weaker form of the Cramér-Rao bound, which does not require the inversion of the QFIM. It is desirable to understand how relevant these weaker bounds are and how closely they approach the exact Cramér-Rao bounds. We thus analyze the reason for this singularity and, by removing a redundant phase, obtain a nonsingular QFIM, allowing us to derive exact quantum Cramér-Rao bounds. Using the nonsingular QFIM, we show that the arithmetic average of the distributed phases is Heisenberg limited. We demonstrate that quantum metrological bounds can be saturated by projective measurements, enabling us to determine the Fisher information matrix, which is also singular. We then show how this singularity can be resolved.

View Accepted Manuscript (DOE)

Research Organization:: Texas A&M University, College Station, TX (United States)

Sponsoring Organization:: Air Force Office of Scientific Research (AFOSR); USDOE Office of Science (SC), Biological and Environmental Research (BER). Biological Systems Science (BSS)

Grant/Contract Number:: AC36-08GO28308

OSTI ID:: 2497739

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 1 Vol. 111; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (60)

Generalized Uncertainty Relations: Theory, Examples, and Lorentz Invariance Braunstein, Samuel L.; Caves, Carlton M.; Milburn, G. J. Annals of Physics, Vol. 247, Issue 1 https://doi.org/10.1006/aphy.1996.0040	journal	April 1996
Quantum detection and estimation theory Helstrom, Carl W. Journal of Statistical Physics, Vol. 1, Issue 2 https://doi.org/10.1007/BF01007479	journal	January 1969
Monotone metrics on matrix spaces Petz, Dénes Linear Algebra and its Applications, Vol. 244 https://doi.org/10.1016/0024-3795(94)00211-8	journal	September 1996
Minimum mean-squared error of estimates in quantum statistics Helstrom, C. W. Physics Letters A, Vol. 25, Issue 2 https://doi.org/10.1016/0375-9601(67)90366-0	journal	July 1967
Quantum Fisher metric and estimation for pure state models Fujiwara, Akio; Nagaoka, Hiroshi Physics Letters A, Vol. 201, Issue 2-3 https://doi.org/10.1016/0375-9601(95)00269-9	journal	May 1995
Uncertainty relations for joint measurements of noncommuting observables Ozawa, Masanao Physics Letters A, Vol. 320, Issue 5-6 https://doi.org/10.1016/j.physleta.2003.12.001	journal	January 2004
Symmetric logarithmic derivative for general n-level systems and the quantum Fisher information tensor for three-level systems Ercolessi, E.; Schiavina, M. Physics Letters A, Vol. 377, Issue 34-36 https://doi.org/10.1016/j.physleta.2013.06.012	journal	November 2013
A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging Albarelli, F.; Barbieri, M.; Genoni, M. G. Physics Letters A, Vol. 384, Issue 12 https://doi.org/10.1016/j.physleta.2020.126311	journal	April 2020
Heisenberg's uncertainty principle Busch, P.; Heinonen, T.; Lahti, P. Physics Reports, Vol. 452, Issue 6 https://doi.org/10.1016/j.physrep.2007.05.006	journal	November 2007
XXI.—On the Dominance Ratio Fisher, R. A. Proceedings of the Royal Society of Edinburgh, Vol. 42 https://doi.org/10.1017/S0370164600023993	journal	January 1923
Creation of a six-atom ‘Schrödinger cat’ state Leibfried, D.; Knill, E.; Seidelin, S. Nature, Vol. 438, Issue 7068 https://doi.org/10.1038/nature04251	journal	December 2005
Scalable multiparticle entanglement of trapped ions Häffner, H.; Hänsel, W.; Roos, C. F. Nature, Vol. 438, Issue 7068 https://doi.org/10.1038/nature04279	journal	December 2005
Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state Huang, Yun-Feng; Liu, Bi-Heng; Peng, Liang Nature Communications, Vol. 2, Issue 1 https://doi.org/10.1038/ncomms1556	journal	November 2011
Advances in quantum metrology Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo Nature Photonics, Vol. 5, Issue 4 https://doi.org/10.1038/nphoton.2011.35	journal	March 2011
Toward incompatible quantum limits on multiparameter estimation Xia, Binke; Huang, Jingzheng; Li, Hongjing Nature Communications, Vol. 14, Issue 1 https://doi.org/10.1038/s41467-023-36661-3	journal	February 2023
Distributed quantum sensing of multiple phases with fewer photons Kim, Dong-Hyun; Hong, Seongjin; Kim, Yong-Su Nature Communications, Vol. 15, Issue 1 https://doi.org/10.1038/s41467-023-44204-z	journal	January 2024
Flexible entanglement-distribution network with an AlGaAs chip for secure communications Appas, Félicien; Baboux, Florent; Amanti, Maria I. npj Quantum Information, Vol. 7, Issue 1 https://doi.org/10.1038/s41534-021-00454-7	journal	July 2021
A machine learning approach to Bayesian parameter estimation Nolan, Samuel; Smerzi, Augusto; Pezzè, Luca npj Quantum Information, Vol. 7, Issue 1 https://doi.org/10.1038/s41534-021-00497-w	journal	December 2021
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 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
Deterministic multi-qubit entanglement in a quantum network Zhong, Youpeng; Chang, Hung-Shen; Bienfait, Audrey Nature, Vol. 590, Issue 7847 https://doi.org/10.1038/s41586-021-03288-7	journal	February 2021
Distributed quantum sensing with mode-entangled spin-squeezed atomic states Malia, Benjamin K.; Wu, Yunfan; Martínez-Rincón, Julián Nature, Vol. 612, Issue 7941 https://doi.org/10.1038/s41586-022-05363-z	journal	November 2022
On the geometry of mixed states and the Fisher information tensor Contreras, I.; Ercolessi, E.; Schiavina, M. Journal of Mathematical Physics, Vol. 57, Issue 6 https://doi.org/10.1063/1.4954328	journal	June 2016
Geometries of quantum states Petz, Dénes; Sudár, Csaba Journal of Mathematical Physics, Vol. 37, Issue 6 https://doi.org/10.1063/1.531535	journal	June 1996
Error-tradeoff and error-disturbance relations for incompatible quantum measurements Branciard, C. Proceedings of the National Academy of Sciences, Vol. 110, Issue 17 https://doi.org/10.1073/pnas.1219331110	journal	April 2013
Multi-parameter quantum metrology Szczykulska, Magdalena; Baumgratz, Tillmann; Datta, Animesh Advances in Physics: X, Vol. 1, Issue 4 https://doi.org/10.1080/23746149.2016.1230476	journal	July 2016
A new approach to the Cramér-Rao-type bound of the pure-state model Matsumoto, K. Journal of Physics A: Mathematical and General, Vol. 35, Issue 13 https://doi.org/10.1088/0305-4470/35/13/307	journal	March 2002
Distributed quantum sensing enhanced by continuous-variable error correction Zhuang, Quntao; Preskill, John; Jiang, Liang New Journal of Physics, Vol. 22, Issue 2 https://doi.org/10.1088/1367-2630/ab7257	journal	February 2020
Geometry of mixed states for a q-bit and the quantum Fisher information tensor Ercolessi, E.; Schiavina, M. Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 36 https://doi.org/10.1088/1751-8113/45/36/365303	journal	August 2012
Quantum metrology from a quantum information science perspective Tóth, Géza; Apellaniz, Iagoba Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 42 https://doi.org/10.1088/1751-8113/47/42/424006	journal	October 2014
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
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
Neural-Network Heuristics for Adaptive Bayesian Quantum Estimation Fiderer, Lukas J.; Schuff, Jonas; Braun, Daniel PRX Quantum, Vol. 2, Issue 2 https://doi.org/10.1103/PRXQuantum.2.020303	journal	April 2021
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 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
14-Qubit Entanglement: Creation and Coherence Monz, Thomas; Schindler, Philipp; Barreiro, Julio T. Physical Review Letters, Vol. 106, Issue 13 https://doi.org/10.1103/PhysRevLett.106.130506	journal	March 2011
Experimental Ten-Photon Entanglement Wang, Xi-Lin; Chen, Luo-Kan; Li, W. Physical Review Letters, Vol. 117, Issue 21 https://doi.org/10.1103/PhysRevLett.117.210502	journal	November 2016
Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases Pezzè, Luca; Ciampini, Mario A.; Spagnolo, Nicolò Physical Review Letters, Vol. 119, Issue 13 https://doi.org/10.1103/PhysRevLett.119.130504	journal	September 2017
10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit Song, Chao; Xu, Kai; Liu, Wuxin Physical Review Letters, Vol. 119, Issue 18 https://doi.org/10.1103/PhysRevLett.119.180511	journal	November 2017
18-Qubit Entanglement with Six Photons’ Three Degrees of Freedom Wang, Xi-Lin; Luo, Yi-Han; Huang, He-Liang Physical Review Letters, Vol. 120, Issue 26 https://doi.org/10.1103/PhysRevLett.120.260502	journal	June 2018
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
Sensitivity Bounds for Multiparameter Quantum Metrology Gessner, Manuel; Pezzè, Luca; Smerzi, Augusto Physical Review Letters, Vol. 121, Issue 13 https://doi.org/10.1103/PhysRevLett.121.130503	journal	September 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
Incorporating Heisenberg’s Uncertainty Principle into Quantum Multiparameter Estimation Lu, Xiao-Ming; Wang, Xiaoguang Physical Review Letters, Vol. 126, Issue 12 https://doi.org/10.1103/PhysRevLett.126.120503	journal	March 2021
Quantum Metrological Power of Continuous-Variable Quantum Networks Kwon, Hyukgun; Lim, Youngrong; Jiang, Liang Physical Review Letters, Vol. 128, Issue 18 https://doi.org/10.1103/PhysRevLett.128.180503	journal	May 2022
Quantum-Enhanced Metrology with Network States Yang, Yuxiang; Yadin, Benjamin; Xu, Zhen-Peng Physical Review Letters, Vol. 132, Issue 21 https://doi.org/10.1103/PhysRevLett.132.210801	journal	May 2024
Quantum limits on precision measurements of phase Braunstein, Samuel L. Physical Review Letters, Vol. 69, Issue 25 https://doi.org/10.1103/PhysRevLett.69.3598	journal	December 1992
Statistical distance and the geometry of quantum states Braunstein, Samuel L.; Caves, Carlton M. Physical Review Letters, Vol. 72, Issue 22 https://doi.org/10.1103/PhysRevLett.72.3439	journal	May 1994
Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation Pan, Jian-Wei; Daniell, Matthew; Gasparoni, Sara Physical Review Letters, Vol. 86, Issue 20 https://doi.org/10.1103/PhysRevLett.86.4435	journal	May 2001
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
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
Observation of Entangled States of a Fully Controlled 20-Qubit System Friis, Nicolai; Marty, Oliver; Maier, Christine Physical Review X, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevX.8.021012	journal	April 2018
The minimum variance of estimates in quantum signal detection Helstrom, C. IEEE Transactions on Information Theory, Vol. 14, Issue 2 https://doi.org/10.1109/TIT.1968.1054108	journal	March 1968
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
Deep reinforcement learning for quantum multiparameter estimation Cimini, Valeria; Valeri, Mauro; Polino, Emanuele Advanced Photonics, Vol. 5, Issue 01 https://doi.org/10.1117/1.AP.5.1.016005	journal	February 2023
Bell’s theorem without inequalities Greenberger, Daniel M.; Horne, Michael A.; Shimony, Abner American Journal of Physics, Vol. 58, Issue 12 https://doi.org/10.1119/1.16243	journal	December 1990
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit Giovannetti, V. Science, Vol. 306, Issue 5700 https://doi.org/10.1126/science.1104149	journal	November 2004
Entanglement-based quantum information technology: a tutorial Zhang, Zheshen; You, Chenglong; Magaña-Loaiza, Omar S. Advances in Optics and Photonics, Vol. 16, Issue 1 https://doi.org/10.1364/AOP.497143	journal	March 2024
Observation of ten-photon entanglement using thin BiB_3O_6 crystals Chen, Luo-Kan; Li, Zheng-Da; Yao, Xing-Can Optica, Vol. 4, Issue 1 https://doi.org/10.1364/OPTICA.4.000077	journal	January 2017
Multiparameter approach to quantum phase estimation with limited visibility Roccia, Emanuele; Cimini, Valeria; Sbroscia, Marco Optica, Vol. 5, Issue 10 https://doi.org/10.1364/OPTICA.5.001171	journal	January 2018

Similar Records

Quantum Fisher information of the Greenberg-Horne-Zeilinger state in decoherence channels

Journal Article · Mon Aug 15 00:00:00 EDT 2011 · Physical Review. A · OSTI ID:22068495

Remote information concentration by a Greenberger-Horne-Zeilinger state and by a bound entangled state

Journal Article · Fri Aug 01 00:00:00 EDT 2003 · Physical Review. A · OSTI ID:20640112

Optimal detection of entanglement in Greenberger-Horne-Zeilinger states

Journal Article · Mon Feb 14 23:00:00 EST 2011 · Physical Review. A · OSTI ID:21537091

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Quantum measurements
Quantum metrology

Exact quantum Fisher matrix results for distributed phases using multiphoton polarization Greenberger-Horne-Zeilinger states

Citation Formats

References (60)

Similar Records

Related Subjects