Due Wednesday November 3rd:

For Wed:

  1. Write $|-\rangle$ as a linear combination of $|0\rangle$ and $|1\rangle$.
  2. Write $|i\rangle$ as a linear combination of $|+\rangle$ and $|-\rangle$.
  3. Consider the state $|\psi\rangle = \frac{1}{\sqrt{5}} |0\rangle + \frac{2}{\sqrt{5}}|1\rangle$.
      1. Measure it in the basis $|0\rangle$, $|1\rangle$.  What are the possible outcomes and their probabilities?
      2. 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 linear combination of $|+\rangle$ and $|-\rangle$.)
  4. Time permitting, do this problem.