Non-asymptotic quantum metrology
arXiv:1912.02324
Abstract
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a methodology that departs from asymptotic approximations and restricted parameter locations, while practical convenience requires that it is also flexible and easy to use in applications with limited data. We submit that this methodology can and should be built on a Bayesian framework, and in this thesis we propose, construct, explore and exploit a new non-asymptotic quantum metrology. First we show the consistency of taking those solutions that are optimal in the asymptotic regime of many trials as a guide to calculate a Bayesian measure of uncertainty. This provides an approximate but useful way of studying the non-asymptotic regime whenever an exact optimisation is intractable, and it avoids the non-physical results that can arise when only the asymptotic theory is used. Secondly, we construct a new non-asymptotic Bayesian bound without relying on the previous approximation by first selecting a single-shot optimal quantum strategy, and then simulating a sequence of repetitions of this scheme. These methods are then applied to a single-parameter Mach-Zehnder interferometer, and to multi-parameter qubit and optical sensing networks. Our results provide a detailed characterisation of how the interplay between prior information, correlations and a limited amount of data affects the performance of quantum metrology protocols, which opens the door to a vast set of unexplored possibilities to enhance non-asymptotic schemes. Finally, we provide practical researchers with a numerical toolbox for Bayesian metrology, while theoretical workers will benefit from the broader and more fundamental perspective that arises from the unified character of our methodology.
PhD thesis, 9 chapters, 3 appendices, 23 figures, 9 tables. Defended on 18 Sep 2019. Published in https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.801042/. Codes available in https://github.com/jesus-rubiojimenez/QuMetrology-finite/. It incorporates, but is not limited to, arXiv:1707.05022, arXiv:1810.12857, arXiv:1906.04123 and part of arXiv:1812.01032
References in corpus (30)
- Satellite-to-ground quantum key distribution
- The European Quantum Technologies Roadmap
- Optimal Quantum Phase Estimation
- Microwave Quantum Illumination
- Quantum Illumination at the Microwave Wavelengths
- Optimal measurements for simultaneous quantum estimation of multiple phases
- Quantum Non-Demolition Detection of Strongly Correlated Systems
- True precision limits in quantum metrology
- All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry
- Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology
- Quantum interferometry with three-dimensional geometry
- Local and Global Distinguishability in Quantum Interferometry
- Bayesian multi-parameter quantum metrology with limited data
- Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks
- Quantum correlations in optical metrology: Heisenberg-limited phase estimation without mode entanglement
- Optimal estimation of entanglement
- Phase sensitivity bounds for two-mode interferometers
- Quantum multi-parameter estimation with generalized balanced multi-mode NOON-like states
- Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates
- Distributed Quantum Metrology with a Single Squeezed-Vacuum Source
- Valid lower bound for all estimators in quantum parameter estimation
- Optimal estimation of the optomechanical coupling strength
- Breaking the weak Heisenberg limit
- Networked quantum sensing
- Improving the precision of frequency estimation via long-time coherences
- Quantum Fisher information for general spatial deformations of quantum emitters
- Entropic Heisenberg limits and uncertainty relations from the Holevo information bound
- From Propositional Logic to Plausible Reasoning: A Uniqueness Theorem
- Entanglement-Enhanced Lidars for Simultaneous Range and Velocity Measurements
- Joint estimation of phase and phase diffusion for quantum metrology