= Solution
Use the <Pauli X eigenstates> $|\pm\rangle=(|0\rangle\pm|1\rangle)/\sqrt2$ and $\cos\theta+i\sin\theta=e^{i\theta}$. Their <probability amplitudes> are
$$
\langle\pm|\phi\rangle=\frac{\sqrt2\pm e^{i\theta}}{\sqrt6}.
$$
The <Born rule> gives
$$
\boxed{\Pr(+)=\frac12+\frac{\sqrt2}{3}\cos\theta,\qquad
\Pr(-)=\frac12-\frac{\sqrt2}{3}\cos\theta.}
$$
The two <probabilities> sum to one. Their dependence on the <relative quantum phase> is the <quantum interference> between the two components in the <computational basis>.
Back to article page
