Probing Bayesian Credible Regions Intrinsically: A Feasible Error Certification for Physical Systems

Changhun Oh, Yong Siah Teo, and Hyunseok Jeong
Phys. Rev. Lett. 123, 040602 – Published 26 July 2019

Abstract

Standard computation of size and credibility of a Bayesian credible region for certifying any point estimator of an unknown parameter (such as a quantum state, channel, phase, etc.) requires selecting points that are in the region from a finite parameter-space sample, which is infeasible for a large dataset or dimension as the region would then be extremely small. We solve this problem by introducing the in-region sampling theory to compute both region qualities just by sampling appropriate functions over the region itself using any Monte Carlo sampling method. We take in-region sampling to the next level by understanding the credible-region capacity (an alternative description for the region content to size) as the average lp-norm distance (p>0) between a random region point and the estimator, and present analytical formulas for p=2 to estimate both the capacity and credibility for any dimension and a sufficiently large dataset without Monte Carlo sampling, thereby providing a quick alternative to Bayesian certification. All results are discussed in the context of quantum-state tomography.

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  • Received 10 February 2019
  • Revised 20 June 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.040602

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Changhun Oh1, Yong Siah Teo1,*, and Hyunseok Jeong1

  • 1Department of Physics and Astronomy, Seoul National University, 08826 Seoul, Korea

  • *ys_teo@snu.ac.kr

See Also

Efficient Bayesian credible-region certification for quantum-state tomography

Changhun Oh, Yong Siah Teo, and Hyunseok Jeong
Phys. Rev. A 100, 012345 (2019)

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Vol. 123, Iss. 4 — 26 July 2019

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