# Daily due November 13th, 2023:

1. I’ve posted solutions to the last daily post in the overleaf document, currently Section 6.4.  Please look these over!
2. I’ve posted some example practice problems for entanglement in Section 6.8.  Please attempt these and compare to the given answers.
3. Can you measure the first qubit of the state $\frac{1}{\sqrt{2}} |00 \rangle + \frac{1}{\sqrt{2}}|01 \rangle$ and get $1$?
4. Consider the quantum state $\frac{1}{2} |00 \rangle + \frac{1}{2} |01 \rangle + \frac{1}{2} |10 \rangle + \frac{1}{2} |11 \rangle$.  Is this entangled?
5. Measure the quantum state $\frac{2}{\sqrt{7}} |00 \rangle + \frac{1}{\sqrt{7}} |01 \rangle + \frac{1}{\sqrt{7}} |10 \rangle + \frac{1}{\sqrt{7}} |11 \rangle$ in the first coordinate.  What are the probabilities of the possible results, and the resulting quantum states?
6. Apply the Pauli Y gate to the state $\frac{1}{\sqrt{5}} |0\rangle + \frac{2}{\sqrt{5}} |1 \rangle$.  What is the result?
7. Check that the Hadamard gate is unitary.
8. Apply the CNOT gate to the state $\frac{1}{\sqrt{5}}|00\rangle + \frac{2}{\sqrt{5}} |11 \rangle$.  What is the result?