Helstrom measurement for the zero and plus states
= Helstrom measurement for the zero and plus states
{c}
For equiprobable states $|0\rangle$ and
$$
|+\rangle=\frac{|0\rangle+|1\rangle}{\sqrt2},
$$
the orthonormal measurement basis at angle $\beta=-\pi/8$ to the computational basis attains
$$
P_s=\frac12\left(1+\frac1{\sqrt2}\right).
$$