Alice and Bob share a state a| + +> + b |- -> , where the first qubit is Alice's and the second qubit is Bob's. Alice measures her qubit in the standard basis and sends the measurement outcome to Bob. If Bob wants his qubit to end up in the state a |0> + b |1>, what gates does he apply to his qubit in the following two cases? Write your answer in terms of X Z H I using comma as a delimiter. (For example, you may write X if the answer is a single gate X , or you can write H,X,Z if the answer is to apply H first, and then Y , and then Z .)
a) When Alice's outcome was 0
b) When Alice's outcome was 1
a) H
im si=ooo hi=orny
To get the desired state a|0> + b|1>, Bob needs to perform specific gates on his qubit based on Alice's measurement outcome.
a) When Alice's outcome was 0:
Bob needs to keep his qubit unchanged because Alice's outcome of 0 means she measured the state |0> with 100% probability. So, Bob doesn't need to do anything. The answer is I (identity gate).
b) When Alice's outcome was 1:
Bob needs to apply the X gate to his qubit because Alice's outcome of 1 means she measured the state |1> with 100% probability. The X gate flips the state from |1> to |0>. So, the answer is X.
Therefore, the answers to the two cases are:
a) I
b) X