Existence of unbiased resilient estimators in discrete quantum systems
arXiv:2402.15242 · doi:10.1103/PhysRevResearch.7.023060
Abstract
The Cramér-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing the optimal unbiased estimator. In contrast, Bhattacharyya bounds offer a more robust estimation framework with respect to prior accuracy by introducing additional constraints on the estimator. In this work, we examine divergences that arise in the computation of these bounds and establish the conditions under which they remain valid. Notably, we show that when the number of constraints exceeds the number of measurement outcomes, an estimator with finite variance typically does not exist. Furthermore, we systematically investigate the properties of these bounds using paradigmatic examples, comparing them to the Cramér-Rao and Bayesian approaches.
Close to the published version
References in corpus (23)
- Advances in Quantum Metrology
- Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light
- Quantum metrology from a quantum information science perspective
- Quantum Illumination with Gaussian States
- Quantum limits in optical interferometry
- Multi-parameter estimation beyond Quantum Fisher Information
- Thermometry in the quantum regime: Recent theoretical progress
- Sensitivity Bounds for Multiparameter Quantum Metrology
- True precision limits in quantum metrology
- Quantum Estimation Methods for Quantum Illumination
- Using polarons for sub-nK quantum non-demolition thermometry in a Bose-Einstein condensate
- Squeezing the quantum noise of a gravitational-wave detector below the standard quantum limit
- -Corrected Heisenberg Limit
- Frequentist and Bayesian Quantum Phase Estimation
- Ultimate accuracy limit of quantum pulse-compression ranging
- Quantum-enhanced Doppler lidar
- Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound
- Quantum Illumination with a Hetero-Homodyne Receiver and Sequential Detection
- Heisenberg-Limited Quantum Lidar for Joint Range and Velocity Estimation
- Strongly coupled fermionic probe for nonequilibrium thermometry
- Hierarchies of Frequentist Bounds for Quantum Metrology: From Cramér-Rao to Barankin
- First-principles construction of symmetry-informed quantum metrologies
- Bhattacharyya inequality for quantum state estimation