2017/01/22 by Bash, Boulat A., Gagatsos, Christos N., Datta, Animesh +1
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1701.06206
We present a square root law for active sensing of phase θ of a single pixel using optical probes that pass through a single-mode lossy thermal-noise bosonic channel. Specifically, we show that, when the sensor uses an n-mode covert optical probe, the mean squared error (MSE) of the resulting estimator θn scales as ⟨ (θ-θn)2⟩=O(1/√(n)); improving the scaling necessarily leads to detection by the adversary with high probability. We fully characterize this limit and show that it is achievable using laser light illumination and a heterodyne receiver, even when the adversary captures every photon that does not return to the sensor and performs arbitrarily complex measurement as permitted by the laws of quantum mechanics.