Quantum Estimation Methods for Quantum Illumination

Quantum illumination consists in shining quantum light on a target region immersed in a bright thermal bath with the aim of detecting the presence of a possible low-reflective object. If the signal is entangled with the receiver, then a suitable choice of the measurement offers a gain with respect to the optimal classical protocol employing coherent states. Here, we tackle this detection problem by using quantum estimation techniques to measure the reflectivity parameter of the object, showing an enhancement in the signal-to-noise ratio up to 3 dB with respect to the classical case when implementing only local measurements. Our approach employs the quantum Fisher information to provide an upper bound for the error probability, supplies the concrete estimator saturating the bound, and extends the quantum illumination protocol to non-Gaussian states. As an example, we show how Schrödinger’s cat states may be used for quantum illumination.

Figure 1

Scheme of the quantum illumination protocol. (a) An entangled state, e.g., a two-mode squeezed state, is generated in the lab. The idler beam stays in a controlled transmission line while the signal is emitted toward the object we want to detect. Since its reflectivity is small, $\eta \ll 1$, most of the light captured by the receiver is thermal noise. By measuring the correlations between the signal and the idler beams, it is possible to detect the presence of an object with a smaller error probability than protocols involving classical light, with a gain up to 3 dB in the error probability exponent.

Figure 2

We plot the gain in the quantum Fisher information $H$ for the Gaussian state (red solid line) and Schrödinger’s cat states (dashed lines), versus the classical case $H_C$ corresponding to a coherent state transmitter. The lines corresponds to the case $N_B=50$. Both Gaussian and Schrödinger’s cat states achieve the maximum gain in the low photon regime, but the former are sizably more stable. The calculation for the Gaussian state is exact, see Eq. (6), while the QFI for the Schrödinger’s cat states has been calculated numerically by truncating the Hilbert space of the received signal. This has been done by checking the convergence of the QFI for increasing Hilbert space dimension.