论文标题
范围和速度的量子限制估计
Quantum-limited estimation of range and velocity
论文作者
论文摘要
能源时间不确定性关系对范围和速度的估计雷达和激光雷达的精度构成了基本限制。目标（通过到达时间）和目标的速度（通过多普勒频移）的估计中的精度彼此相互关系，并取决于信号的带宽。在这里，我们使用多参数量子计量的理论工具箱来确定范围和速度同时估计的最终精度。我们考虑一个单个目标的情况以及一对紧密分离的目标。在后一种情况下，我们专注于相对位置和速度。我们表明，对于纠缠探针状态，估计位置和速度的估计精度之间的权衡是放宽的，并且在无限纠缠的极限中完全取消。在两个目标彼此接近的制度中，使用由对称对数衍生物确定的测量值，相对位置和速度也几乎可以最佳地估算，即使没有纠缠。
The energy-time uncertainty relation puts a fundamental limit on the precision of radars and 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 dictated by the bandwidth of the signal. Here we use the theoretical toolbox of multi-parameter 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 trade-off between the estimation precision of position and velocity is relaxed for entangled probe states, and is completely lifted in the limit of infinite entanglement. 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.
