- #1

ARoyC

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- Homework Statement
- Please check the attached screenshots for the questions.

- Relevant Equations
- Spectral Decomposition of Y, Probability of a Measurement Outcome and Posterior State Formula

**[Mentor Note: Two similar thread starts merged]**

The questions are from MIT OCW. First of all, I cannot understand what is the meaning of the measurement outcome being 0. How can an eigenvalue be 0? I tried doing the problems guessing that by 0 they mean the posterior state will be |0>. The only correct answer I got was for the first part of the second problem. I first wrote the state of the first qubit after passing through the first Hadamard gate. Then I wrote the tensor product state of the two qubits. After that, I applied the cNOT gate on the second qubit and then again the Hadamard gate on the first qubit. Then I used Born Rule to find the probability of the first qubit being in |0>. But I cannot get the answer for the other two parts using this method. Same problem for the first question.

It would be great if someone can help me out. Thank you in advance.

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