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  • Open Access

Quantum estimation of Chernoff bound and Hoeffding bound

Honglin Chen1, Jicun Li1, Wei Xie1,*, and Xiang-Yang Li1,2,†

  • *Contact author: xxieww@ustc.edu.cn
  • †Contact author: xiangyangli@ustc.edu.cn
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Phys. Rev. Research 7, 033245 – Published 12 September, 2025

DOI: https://doi.org/10.1103/blvt-zrww

Abstract

Determining the closeness of two quantum states with minimal error probability is a central problem in quantum information theory. The optimal exponents characterizing the error probability in the symmetric and asymmetric settings are given by the quantum Chernoff bound (QCB) and the quantum Hoeffding bound (QHB), respectively. In this work, we introduce the first algorithms for estimating the QCB and QHB of two unknown states. We propose a unitary encoding for diagonal density matrix based on the copy matrix, which enables unbiased estimation of nonlinear matrix functions via quantum singular value transformation (QSVT). For general density matrices, we combine QSVT with the Hadamard test to estimate both QCB and QHB. Numerical simulations demonstrate that the algorithm converges to the optimal value within a limited number of iterations. Furthermore, we establish the first integration of QSVT with convex optimization, yielding a hybrid quantum-classical framework for quantum estimation.

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Phys. Rev. Research 7, 033245– Published 12 September, 2025
  • Received 27 April 2025
  • Accepted 27 August 2025
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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.

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