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Tight Bounds on the Simultaneous Estimation of Incompatible Parameters

Sidhu, Jasminder S. and Ouyang, Yingkai and Campbell, Earl T. and Kok, Pieter (2021) Tight Bounds on the Simultaneous Estimation of Incompatible Parameters. Physical Review X, 11 (1). Art. No. 011028. ISSN 2160-3308.

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The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables greatly diminishes the applicability of estimation theory in many practical implementations. The Holevo Cramér-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multiparameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimization over multiple variables. In this work, we develop an analytic approach to solving the HCRB for two parameters. Our analysis reveals the role of the HCRB and its interplay with alternative bounds in estimation theory. For more parameters, we generate a lower bound to the HCRB. Our work greatly reduces the complexity of determining the HCRB to solving a set of linear equations that even numerically permits a quadratic speedup over previous state-of-the-art approaches. We apply our results to compare the performance of different probe states in magnetic field sensing and characterize the performance of state tomography on the code space of noisy bosonic error-correcting codes. The sensitivity of state tomography on noisy binomial code states can be improved by tuning two coding parameters that relate to the number of correctable phase and amplitude damping errors. Our work provides fundamental insights and makes significant progress toward the estimation of multiple incompatible observables.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Sidhu, Jasminder S.0000-0002-6167-8224
Ouyang, Yingkai0000-0003-1115-0074
Campbell, Earl T.0000-0002-3903-2734
Additional Information:© 2021 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 4 February 2020; revised 26 November 2020; accepted 24 December 2020; published 11 February 2021. J. S. S. and P. K. acknowledge the support of Engineering and Physical Sciences Research Council (EPSRC) via the Quantum Communications Hub through Grant No. EP/M013472/1. Y. O. and E. T. C. acknowledge the support of EPSRC through Grant No. EP/M024261/1. This work was completed and submitted when E. T. C. was working at the University of Sheffield.
Group:AWS Center for Quantum Computing
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/M013472/1
Engineering and Physical Sciences Research Council (EPSRC)EP/M024261/1
Issue or Number:1
Record Number:CaltechAUTHORS:20210212-133109987
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108041
Deposited By: Tony Diaz
Deposited On:12 Feb 2021 22:14
Last Modified:12 Feb 2021 22:14

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