Maximum advantage of quantum illumination

Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another. Computing the error probability directly requires complete knowledge and diagonalization of the density matrices describing these states. Both of these fundamental requirements become impractically difficult to obtain as the dimensions of the states grow large. In this paper, we analyze quantum illumination as a quantum channel discrimination protocol and circumvent these issues by using the normalized Hilbert-Schmidt inner product as a measure of distinguishability. Using this measure, we show that the greatest advantage gained by quantum illumination over conventional illumination occurs when one uses a Bell state.

Figure 1

Top: Diagram of conventional illumination of the target using conventional (separable states of) light. Bottom: Diagram of quantum illumination of the target with entangled states of light. In the case of an entangled source, joint detection is performed between the held idler and returned noisy signal.