Fundamental limits of quantum-secure covert optical sensing

Abstract

We present a square root law for active sensing of phase $\theta$ 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 ${\hat{\theta }}_n$ scales as $⟨(\theta -{\hat{\theta }}_n{)}^2⟩=\mathcal{O}(1/\sqrt{n})$; 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.

13 pages, 1 figure, submitted to ISIT 2017