Quantum-Limited Estimation of Range and Velocity

The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for estimation range velocity. in (through time arrival) velocity Doppler frequency shifts) target are inversely related to each other, dictated by bandwidth signal. Here we use theoretical toolbox multi-parameter quantum metrology determine ultimate simultaneous We consider case single as well pair closely separated targets. In latter case, focus relative position show that trade-off between is relaxed entangled probe states, completely lifted infinite entanglement. regime where two targets close can be estimated nearly optimally jointly, even without entanglement, using measurements determined symmetric logarithmic derivatives.