Covert sensing using floodlight illumination

We propose a scheme for covert active sensing using floodlight illumination from a terahertz-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 narrow-band 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 or extendible for various practical optical sensing applications.

Figure 1

Alice splits the output of the source on a highly unbalanced beam splitter with controllable transmissivity $\tau$. She sends the weaker of the two beams along a forward propagation path, a single-mode bosonic channel $C_1({\eta }_1,{\overline{n}}_{{\mathrm{B}}_1})$ of transmissivity ${\eta }_1$ and additive thermal noise of mean photon number ${\overline{n}}_{{\mathrm{B}}_1}$ per mode. The propagated light, after accruing an unknown target phase $\theta$, propagates back to Alice on a single-mode bosonic channel $C_1({\eta }_2,{\overline{n}}_{{\mathrm{B}}_2})$. The brighter of the two beams at the transmitter is held locally for use as local oscillator to heterodyne detect the target-return light. All the lost photons on both the forward and return path channels are given to Willie, who is allowed to make an arbitrary quantum measurement.

Figure 2

For the setup of Fig. 1, Alice sees one effective thermal channel $C_{\mathrm{eff}}$. This setup was used in [22] for covert sensing with a coherent-state probe.

Figure 3

Plot of $c_{\mathrm{ASE}}$ as a function of center frequency of transmission, $f$, for three different values of target range, $L$. We used $r_t=4$ cm, $r_T=10$ cm, and $\epsilon ={10}^{-3}$. The shaded area is where the minima appear.

Figure 4

A layout of the setup, equivalent to the one of the main paper, but more explanatory regarding the transformations. The light gray area (A) belongs to Alice, while the darker gray area (W) belongs to Willie.

Figure 5

The heterodyne detection takes place in the gray area. Bold vertical lines represent balanced beam splitters. Alice splits her local oscillator and the sensing arm into two equal beams each. On the lower local oscillator a phase $\pi /2$ is applied. Then, modes (1) and (2) of the sensing arm are mixed with modes (3) and (4), respectively. Finally, a homodyne is performed on the couples of modes (1) and (3) and modes (2) and (4) using photon number resolution detectors.