Quantum-Limited Estimation of Range and Velocity

被引:19
|
作者
Huang, Zixin [1 ,2 ]
Lupo, Cosmo [1 ]
Kok, Pieter [1 ]
机构
[1] Univ Sheffield, Dept Phys & Astron, Sheffield S3 7RH, S Yorkshire, England
[2] Macquarie Univ, Ctr Engn Quantum Syst, Dept Phys & Astron, Sydney, NSW 2109, Australia
来源
PRX QUANTUM | 2021年 / 2卷 / 03期
基金
英国工程与自然科学研究理事会;
关键词
Frequency estimation - Quantum entanglement;
D O I
10.1103/PRXQuantum.2.030303
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
收藏
页数:18
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