title: Precision metrology using weak measurements.
abstract: Weak values and measurements have been proposed as a means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur with highly suppressed probabilities. This raises three vital questions in weak-measurement-based metrology. Namely, (Q1) Does postselection enhance the measurement precision? (Q2) Does weak measurement offer better precision than strong measurement? (Q3) Is it possible to beat the standard quantum limit or to achieve the Heisenberg limit with weak measurement using only classical resources? We analyze these questions for two prototypical, and generic, measurement protocols and show that while the answers to the first two questions are negative for both protocols, the answer to the last is affirmative for measurements with phase-space interactions, and negative for configuration space interactions. Our results, particularly the ability of weak measurements to perform at par with strong measurements in some cases, are instructive for the design of weak-measurement-based protocols for quantum metrology.
authors.affiliation: National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China.|Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.|Max Planck Institute for Structure and Dynamics of Material, Hamburg 22761, Germany.
authors.forename: Lijian
authors.initials: L
authors.lastname: Zhang
authors.affiliation: Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom.|Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom.
authors.forename: Animesh
authors.initials: A
authors.lastname: Datta
authors.affiliation: Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom.
authors.forename: Ian A
authors.initials: IA
authors.lastname: Walmsley