Optimal probes for continuous-variable quantum illumination

Abstract

Quantum illumination is the task of determining the presence of an object in a noisy environment. We determine the optimal continuous-variable states for quantum illumination in the limit of zero object reflectivity. We prove that the optimal single-mode state is a coherent state, while the optimal two-mode state is the two-mode squeezed-vacuum state. We find that these probes are not optimal at nonzero reflectivity, but remain near optimal. This demonstrates the viability of the continuous-variable platform for an experimentally accessible, near optimal quantum illumination implementation.

Quantum illumination with a light absorbing target

“…Let us now move to the scenario of quantum illumination process where two mode states are considered as probes. It was shown that for a low reflectivity, TMSV state act as an optimal probe in the no-absorbing domain [11,36]. We will now show that the TMSV state still remains optimal in the absorbing regime.…”

“…Both the axes are dimensionless. to be the optimal two mode probe state for detecting a nonabsorbing target [36]. It was also proven that it can outperform the coherent state-based illumination protocol in the low signal strength and high background noise limit [9], thereby establishing the quantum advantage.…”

“…where κ → 0 is the low reflectivity and r → 0 represents the low loss approximation. δρ a is given by ∂ρ 1 /∂ √ κ| κ→0 while δρ b = ∂ρ 1 /∂ √ r| r→0 , δρ b = 1 2 ∂ρ 1 /∂r| r→0 and δρ c = ∂ρ 1 /∂ √ rκ| κ,r→0 [36]. At the end of our calculations, we take → 1.…”

“…In case of a lossless target, the single mode optimal probe is known to be the coherent state [11,36]. Let us now identify the optimal probes for detecting a target modelled by a lossy beam splitter.…”

“…we can consider the C n s to be real. Thus, subject to the normalisation ( n C 2 n = 1) and the energy ( n nC 2 n = N S ) constraints, the maximization condition for ζ reduces to [36]…”