Consider the pure state $|\psi\rangle=\frac{|0\rangle+|1\rangle}{\sqrt{2}}$, and the mixed state obtained by tossing a coin and setting it equal to $|0\rangle$ if the result is heads, or $|1\rangle$ if the result is tails. ${ }^3$ Devise an experiment that discriminates between these two states.
$$
\left\{\frac{|0\rangle+|1\rangle}{\sqrt{2}}, \frac{|0\rangle-|1\rangle}{\sqrt{2}}\right\}
$$