  It is well known that the Helstrom bound can be improved by generalizing the
form of a coherent state. Thus, designing a quantum measurement achieving the
improved Helstrom bound is important for novel quantum communication. In the
present article, we analytically show that the improved Helstrom bound can be
achieved by a projective measurement composed of orthogonal non-standard
Schr\"{o}dinger cat states. Moreover, we numerically show that the improved
Helstrom bound can be nearly achieved by an indirect measurement based on the
Jaynes-Cummings model. As the Jaynes-Cummings model describes an interaction
between a light and a two-level atom, we emphasize that the indirect
measurement considered in this article has potential to be experimentally
implemented.
