# The maximum advantage of quantum illumination. (arXiv:1902.05587v1 [quant-ph])

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

dimension of the states grow large. In this article, 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.