Huang, Z., Lupo, C. orcid.org/0000-0002-5227-4009 and Kok, P. (2021) Quantum-limited estimation of range and velocity. PRX Quantum, 2 (3). 030303. ISSN 2691-3399
Abstract
The energy-time uncertainty relation puts a fundamental limit on the precision of lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity (through Doppler frequency shifts) of a target are inversely related to each other and are dictated by the bandwidth of the signal. Here, we use the theoretical toolbox of multiparameter quantum metrology to determine the ultimate precision of the simultaneous estimation of range and velocity. We consider the case of a single target as well as a pair of closely separated targets. In the latter case, we focus on the relative position and velocity. We show that the tradeoff between the estimation precision of position and velocity is relaxed for entangled probe states and is completely lifted in the limit of perfect photon time-frequency correlations. In the regime where the two targets are close to each other, the relative position and velocity can be estimated nearly optimally and jointly, even without entanglement, using the measurements determined by the symmetric logarithmic derivatives.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2021 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0/). Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/M013472/1 Engineering and Physical Sciences Research Council EP/T001011/1 Engineering and Physical Sciences Research Council 2284102 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL UNSPECIFIED ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/V021303/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Jul 2021 12:09 |
Last Modified: | 16 Jul 2021 12:09 |
Status: | Published |
Publisher: | American Physical Society (APS) |
Refereed: | Yes |
Identification Number: | 10.1103/prxquantum.2.030303 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:176267 |