Valid lower bound for all estimators in quantum parameter estimation
arXiv:1609.01618 · doi:10.1088/1367-2630/18/9/093009
Abstract
The widely used quantum Cramer-Rao bound (QCRB) sets a lower bound for the mean square error of unbiased estimators in quantum parameter estimation, however, in general QCRB is only tight in the asymptotical limit. With a limited number of measurements biased estimators can have a far better performance for which QCRB cannot calibrate. Here we introduce a valid lower bound for all estimators, either biased or unbiased, which can serve as standard of merit for all quantum parameter estimations.
9 pages, 5 figures
References in corpus (22)
- Advances in Quantum Metrology
- Quantum metrology
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Quantum metrology from a quantum information science perspective
- The elusive Heisenberg limit in quantum enhanced metrology
- Generalized uncertainty relations: Theory, examples, and Lorentz invariance
- Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
- State estimation for large ensembles
- Quantum metrology for a general Hamiltonian parameter
- Phase matching condition for enhancement of phase sensitivity in quantum metrology
- Quantum Metrological Limits via a Variational Approach
- Ziv-Zakai Error Bounds for Quantum Parameter Estimation
- Universal time scaling for Hamiltonian parameter estimation
- Quantum metrology with open dynamical systems
- Quantum metrology with unitary parametrization processes
- Phase Sensitivity of a Mach-Zehnder Interferometer
- Quantum measurement bounds beyond the uncertainty relations
- Quantum multiparameter metrology with generalized entangled coherent state
- Phase sensitivity bounds for two-mode interferometers
- Multiple phase estimation for arbitrary pure states under white noise
- True Limits to Precision via Unique Quantum Probe
- Distribution of quantum Fisher information in asymmetric cloning machines
Cited by in corpus (13)
- Quantum Fisher information matrix and multiparameter estimation
- Quantum enhanced measurements without entanglement
- Control-enhanced multiparameter quantum estimation
- Quantum Semiparametric Estimation
- Optimal Scheme for Quantum Metrology
- Review: Quantum Metrology and Sensing with Many-Body Systems
- QuanEstimation: An open-source toolkit for quantum parameter estimation
- Universal cost bound of quantum error mitigation based on quantum estimation theory
- Achieving Heisenberg scaling with maximally entangled states: an analytic upper bound for the attainable root mean square error
- Conservative classical and quantum resolution limits for incoherent imaging
- Current Trends in Global Quantum Metrology
- Bayesian estimation for collisional thermometry
- Non-asymptotic quantum metrology