Fundamental limits of quantum-secure covert optical sensing

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 $\langle (\theta-\hat{\theta}_n)^2\rangle=\mathcal{O}(1/\sqrt{n})$; 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.Comment: 13 pages, 1 figure, submitted to ISIT 201

Covert sensing using floodlight illumination

We propose a scheme for covert active sensing using floodlight illumination from a THz-bandwidth amplified spontaneous emission (ASE) source and heterodyne detection. We evaluate the quantum-estimation-theoretic performance limit of covert sensing, wherein a transmitter's attempt to sense a target phase is kept undetectable to a quantum-equipped passive adversary, by hiding the signal photons under the thermal noise floor. Despite the quantum state of each mode of the ASE source being mixed (thermal), and hence inferior compared to the pure coherent state of a laser mode, the thousand-times higher optical bandwidth of the ASE source results in achieving a substantially superior performance compared to a narrowband laser source by allowing the probe light to be spread over many more orthogonal temporal modes within a given integration time. Even though our analysis is restricted to single-mode phase sensing, this system could be applicable extendible for various practical optical sensing applications.Comment: We present new results and discuss some results found in arXiv:1701.06206. Comments are welcom

Quantum limits of covert target detection

In covert target detection, Alice attempts to send optical or microwave probes to detect whether or not a weakly-reflecting target embedded in thermal background radiation is present in a target region while remaining undetected herself by an adversary Willie who is co-located with the target and collects all the light that does not return to Alice. We formulate this problem in a realistic setting and derive quantum-mechanical limits on Alice's error probability performance in entanglement-assisted target detection for any fixed level of her detectability by Willie. In particular, we show that Alice must expend a minimum energy in her probe light to maintain a given covertness level, but is also able to achieve a nonzero error probability exponent while remaining perfectly covert. We compare the performance of two-mode squeezed vacuum probes and Gaussian-distributed coherent states to our performance limits. We also obtain quantum limits for discriminating any two thermal loss channels and for non-adversarial quantum illumination without the no-passive-signature assumption.Comment: 18 pages, 5 figure

Quantum-Enhanced Transmittance Sensing

We consider the problem of estimating unknown transmittance $\theta$ of a target bathed in thermal background light. As quantum estimation theory yields the fundamental limits, we employ the lossy thermal-noise bosonic channel model, which describes sensor-target interaction quantum mechanically in many practical active-illumination systems (e.g., using emissions at optical, microwave, or radio frequencies). We prove that quantum illumination using two-mode squeezed vacuum (TMSV) states asymptotically achieves minimal quantum Cram\'{e}r-Rao bound (CRB) over all quantum states (not necessarily Gaussian) in the limit of low transmitted power. We characterize the optimal receiver structure for TMSV input, and show its advantage over other receivers using both analysis and Monte Carlo simulation.Comment: Minor revision, 17 pages, 11 figures. in IEEE J. Sel. Top. Signal Proces