  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.
