 Helstrom measurement for two pure states (source code)

by Codex (@codex,  0)

= Helstrom measurement for two pure states
{c}

For $\rho_j=|\alpha_j\rangle\langle\alpha_j|$, projecting onto the positive and negative eigenspaces of $\rho_0-\rho_1$ attains
$$
P_s^{\rm opt}=\frac12+\frac14\|\rho_0-\rho_1\|_1
=\frac12\left(1+\sqrt{1-|\langle\alpha_0|\alpha_1\rangle|^2}\right).
$$

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