Average number is an insufficient metric for interferometry

Abstract

We argue that analysing schemes for metrology solely in terms of the average particle number can obscure the number of particles effectively used in informative events. For a number of states we demonstrate that, in both frequentist and Bayesian frameworks, the average number of a state can essentially be decoupled from the aspects of the total number distribution associated with any metrological advantage.

References in corpus (52)

• Advances in Quantum Metrology
• Quantum metrology
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
• Quantum metrology from a quantum information science perspective
• Super-resolving phase measurements with a multi-photon entangled state
• The elusive Heisenberg limit in quantum enhanced metrology
• Conversion of conventional gravitational-wave interferometers into QND interferometers by modifying their input and/or output optics
• Biological measurement beyond the quantum limit
• Quantum limits in optical interferometry
• Boson sampling with 20 input photons in 60-mode interferometers at $10^{14}$ state spaces
• Quantum phase estimation with lossy interferometers
• Unconditional violation of the shot noise limit in photonic quantum metrology
• Multi-parameter estimation beyond Quantum Fisher Information
• Optimal quantum-enhanced interferometry using a laser power source
• Quantum interferometry with and without an external phase reference
• Entanglement-enhanced probing of a delicate material system
• Sensitivity Bounds for Multiparameter Quantum Metrology
• Extremal properties of the variance and the quantum Fisher information
• Optimal phase measurements with pure Gaussian states
• Quantum metrology with imperfect states and detectors
• True precision limits in quantum metrology
• Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational-wave detector GEO600
• Ziv-Zakai Error Bounds for Quantum Parameter Estimation
• Entanglement and sensitivity in precision measurements with states of a fluctuating number of particles
• Phase estimation without a priori knowledge in the presence of loss
• All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry
• Bayesian quantum frequency estimation in presence of collective dephasing
• Sub-Heisenberg estimation strategies are ineffective
• Optimal Quantum-Enhanced Interferometry
• Generation of non-classical light in a photon-number superposition
• $\pi$-Corrected Heisenberg Limit
• Does nonlinear metrology offer improved resolution? Answers from quantum information theory
• Universality of the Heisenberg limit for estimates of random phase shifts
• Bayesian multi-parameter quantum metrology with limited data
• Quantum metrology in the presence of limited data
• Quantum correlations in optical metrology: Heisenberg-limited phase estimation without mode entanglement
• Beyond quantum Fisher information: optimal phase estimation with arbitrary a priori knowledge
• Frequentist and Bayesian Quantum Phase Estimation
• Phase sensitivity bounds for two-mode interferometers
• Sub-Heisenberg estimation of non-random phase-shifts
• Quantum Metrology: Extended Convexity of Quantum Fisher Information
• Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates
• Quantum-enhanced stimulated emission microscopy
• Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound
• Spectrum analysis with quantum dynamical systems
• Unbounded quantum Fisher information in two-path interferometry with finite photon number
• Integrated Photonic Sensing
• Non-Orthogonal Bases for Quantum Metrology
• Breaking the weak Heisenberg limit
• Using states with a large photon number variance to increase quantum Fisher information in single-mode phase estimation
• Weakly invasive metrology: quantum advantage and physical implementations