Criteria for unbiased estimation: applications to noise-agnostic sensing and learnability of quantum channel

• URL: http://arxiv.org/abs/2503.17362v1
• Date: Fri, 21 Mar 2025 17:59:48 GMT
• Title: Criteria for unbiased estimation: applications to noise-agnostic sensing and learnability of quantum channel
• Authors: Hyukgun Kwon, Kento Tsubouchi, Chia-Tung Chu, Liang Jiang,
• Abstract summary: We first consider quantum state estimation, where multiple parameters are encoded in a quantum state.<n>We derive two equivalent necessary and sufficient conditions for an unbiased estimation.<n>We extend our analysis to quantum channel estimation, where the goal is to estimate parameters characterizing an unknown quantum channel.
• Score: 1.7635061227370266
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish the necessary and sufficient conditions for unbiased estimation in multi-parameter estimation tasks. More specifically, we first consider quantum state estimation, where multiple parameters are encoded in a quantum state, and derive two equivalent necessary and sufficient conditions for an unbiased estimation: one formulated in terms of the quantum Fisher information matrix (QFIM) and the other based on the derivatives of the encoded state. Furthermore, we introduce a generalized quantum Cram\'er-Rao bound, which provides a fundamental achievable lower bound on the estimation error even when the QFIM is non-invertible. To demonstrate the utility of our framework, we consider phase estimation under unknown Pauli noise. We show that while unbiased phase estimation is infeasible with a naive scheme, employing an entangled probe with a noiseless ancilla enables unbiased estimation. Next, we extend our analysis to quantum channel estimation (equivalently, quantum channel learning), where the goal is to estimate parameters characterizing an unknown quantum channel. We establish the necessary and sufficient condition for unbiased estimation of these parameters. Notably, by interpreting unbiased estimation as learnability, our result applies to the fundamental learnability of parameters in general quantum channels. As a concrete application, we investigate the learnability of noise affecting non-Clifford gates via cycle benchmarking.

Related papers

• Noise-Robust Estimation of Quantum Observables in Noisy Hardware [0.0]
  Noise-Robust Estimation is a noise-agnostic framework that systematically reduces estimation bias.<n>NRE exploits a bias-dispersion correlation uncovered in this work.<n>We experimentally validate NRE on an IQM superconducting quantum processor.
  arXiv  Detail & Related papers  (2025-03-09T17:18:16Z)
• Bayesian Quantum Amplitude Estimation [49.1574468325115]
  We introduce BAE, a noise-aware Bayesian algorithm for quantum amplitude estimation.<n>We show that BAE achieves Heisenberg-limited estimation and benchmark it against other approaches.
  arXiv  Detail & Related papers  (2024-12-05T18:09:41Z)
• The Cramér-Rao approach and global quantum estimation of bosonic states [52.47029505708008]
  It is unclear whether the Cram'er-Rao approach is applicable for global estimation instead of local estimation. We find situations where the Cram'er-Rao approach does and does not work for quantum state estimation problems involving a family of bosonic states in a non-IID setting.
  arXiv  Detail & Related papers  (2024-09-18T09:49:18Z)
• Two-stage Quantum Estimation and the Asymptotics of Quantum-enhanced Transmittance Sensing [2.154235236831441]
  We consider estimation of a single unknown parameter embedded in a quantum state.<n>The measurement required often depends on the true value of the parameter of interest.
  arXiv  Detail & Related papers  (2024-02-27T22:28:42Z)
• Fisher information susceptibility for multiparameter quantum estimation [0.23436632098950458]
  Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit. In quantum metrology, the introduction of the Fisher information measurement noise susceptibility now allows to quantify the robustness of measurement. We provide its mathematical definition in the form of a semidefinite program.
  arXiv  Detail & Related papers  (2023-12-04T16:54:01Z)
• Quantum metrology in the finite-sample regime [0.6299766708197883]
  In quantum metrology, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram'er-Rao bound. We propose to quantify the quality of a protocol by the probability of obtaining an estimate with a given accuracy.
  arXiv  Detail & Related papers  (2023-07-12T18:00:04Z)
• Quantum-enhanced mean value estimation via adaptive measurement [0.39102514525861415]
  Mean value estimation of observables is an essential subroutine in quantum computing algorithms. The quantum estimation theory identifies the ultimate precision of such an estimator, which is referred to as the quantum Cram'er-Rao (QCR) lower bound or equivalently the inverse of the quantum Fisher information. We propose a quantum-enhanced mean value estimation method in a depolarizing noisy environment that saturates the QCR bound in the limit of a large number of qubits.
  arXiv  Detail & Related papers  (2022-10-27T17:13:07Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Dual-Frequency Quantum Phase Estimation Mitigates the Spectral Leakage of Quantum Algorithms [76.15799379604898]
  Quantum phase estimation suffers from spectral leakage when the reciprocal of the record length is not an integer multiple of the unknown phase. We propose a dual-frequency estimator, which approaches the Cramer-Rao bound, when multiple samples are available.
  arXiv  Detail & Related papers  (2022-01-23T17:20:34Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)
• In and out of equilibrium quantum metrology with mean-field quantum criticality [68.8204255655161]
  We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level.
  arXiv  Detail & Related papers  (2020-01-09T19:20:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.