Measure $|+\rangle$ in the $|0\rangle$, $|1\rangle$ basis (i.e. give results and probabilities).

Measure $|+\rangle + i|-\rangle$ in the $|0\rangle$, $|1\rangle$ basis (i.e. give results and probabilities).

Consider the state $|\psi\rangle = \frac{1}{\sqrt{5}} |0\rangle + \frac{2}{\sqrt{5}}|1\rangle$.

Measure it in the basis $|0\rangle$, $|1\rangle$. What are the possible outcomes and their probabilities?

Measure it in the basis $|+\rangle$, $|-\rangle$. What are the possible outcomes and their probabilities? (To do this, you will first need to write $|\psi\rangle$ as a normalized linear combination of $|+\rangle$ and $|-\rangle$.)

With what time remains, work through whatever parts are most useful or interesting to you of this worksheet. My suggestion: if you’re comfortable with the complex numbers as done in class, then start at “Domain Colouring” which is just lovely. If you need more practice with complex numbers because they are new, the earlier parts of the worksheet will provide that.