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 a|+⟩+b|−⟩, what gate does he apply to his qubit in the following two cases? Choose your answer from I,X,Z,H.

When Alice's outcome was 0:
When Alice's outcome was 1:

Please show your work on your previous posts before you post any more.

I

X

I think the same, that in first case you don´t have to do anythin, and in the second case it´s a bit flip, but it is not correct, why? I think it´s because the sign basis used at the begining? So which could be the correct answer?

0 --I,H

what are the answers for 6th a and 6th b questions pls help me

To answer this question, we need to understand the state that Alice and Bob share and the measurement outcomes. Let's break it down step by step:

Alice and Bob share the state a|++⟩ + b|--⟩.
- The first qubit is Alice's, and the second qubit is Bob's.
- This state can be written as a|+⟩⨂|+⟩ + b|-⟩⨂|-⟩.

Alice measures her qubit in the standard basis and sends the outcome to Bob.
- The standard basis consists of the states |0⟩ and |1⟩.

Now let's consider the two cases:

1. When Alice's outcome was 0:
- If Alice measures her qubit in the standard basis and obtains outcome 0, it means that the state collapses to the state |0⟩.
- Since Bob wants the state a|+⟩ + b|-⟩, he wants the second qubit to be in the state |+⟩.
- To achieve this, Bob needs to apply the X gate (Pauli-X gate) to his qubit.
- Therefore, the gate that Bob applies in this case is X.

2. When Alice's outcome was 1:
- If Alice measures her qubit in the standard basis and obtains outcome 1, it means that the state collapses to the state |1⟩.
- Since Bob wants the state a|+⟩ + b|-⟩, he wants the second qubit to be in the state |+⟩.
- To achieve this, Bob needs to apply the X gate (Pauli-X gate) to his qubit.
- Therefore, the gate that Bob applies in this case is X.

In both cases, Bob applies the X gate to his qubit.