Next Article in Journal
Investigation of the Pressure Gain Characteristics and Cycle Performance in Gas Turbines Based on Interstage Bleeding Rotating Detonation Combustion
Next Article in Special Issue
Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
Previous Article in Journal
Quantum Discord, Thermal Discord, and Entropy Generation in the Minimum Error Discrimination Strategy
Previous Article in Special Issue
A Survey of the Concept of Disturbance in Quantum Mechanics
Article Menu
Issue 3 (March) cover image

Export Article

Open AccessArticle
Entropy 2019, 21(3), 264; https://doi.org/10.3390/e21030264

Limiting Uncertainty Relations in Laser-Based Measurements of Position and Velocity Due to Quantum Shot Noise

Bremen Institute for Metrology, Automation and Quality Science (BIMAQ), University of Bremen, Linzer Str. 13, 28359 Bremen, Germany
Received: 24 January 2019 / Revised: 2 March 2019 / Accepted: 5 March 2019 / Published: 8 March 2019
(This article belongs to the Special Issue Entropic Uncertainty Relations and Their Applications)
Full-Text   |   PDF [878 KB, uploaded 8 March 2019]   |  

Abstract

With the ongoing progress of optoelectronic components, laser-based measurement systems allow measurements of position as well as displacement, strain and velocity with unbeatable speed and low measurement uncertainty. The performance limit is often studied for a single measurement setup, but a fundamental comparison of different measurement principles with respect to the ultimate limit due to quantum shot noise is rare. For this purpose, the Cramér-Rao bound is described as a universal information theoretic tool to calculate the minimal achievable measurement uncertainty for different measurement techniques, and a review of the respective lower bounds for laser-based measurements of position, displacement, strain and velocity at particles and surfaces is presented. As a result, the calculated Cramér-Rao bounds of different measurement principles have similar forms for each measurand including an indirect proportionality with respect to the number of photons and, in case of the position measurement for instance, the wave number squared. Furthermore, an uncertainty principle between the position uncertainty and the wave vector uncertainty was identified, i.e., the measurement uncertainty is minimized by maximizing the wave vector uncertainty. Additionally, physically complementary measurement approaches such as interferometry and time-of-flight positions measurements as well as time-of-flight and Doppler particle velocity measurements are shown to attain the same fundamental limit. Since most of the laser-based measurements perform similar with respect to the quantum shot noise, the realized measurement systems behave differently only due to the available optoelectronic components for the concrete measurement task. View Full-Text
Keywords: optical metrology; shot noise limit; measurement uncertainty; Fisher information; estimation theory; Cramér-Rao inequality optical metrology; shot noise limit; measurement uncertainty; Fisher information; estimation theory; Cramér-Rao inequality
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Fischer, A. Limiting Uncertainty Relations in Laser-Based Measurements of Position and Velocity Due to Quantum Shot Noise. Entropy 2019, 21, 264.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top