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I have the following problem:

"Consider two parties: Alice in possession of the one-qubit state |ψ⟩ = α|0⟩ + β|1⟩, and Bob who starts with a qubit in the state |0⟩

Show that Alice can teleport her state |ψ⟩ to Bob using a cnot quantum gate, performing a measurement in the sign basis {|+⟩, |−⟩} on her qubit, and classically communicating one cbit to Bob so he can unitarily act on his qubit based on that information, such that the state is successfully transmitted."

Initially I have the state $|\psi\rangle |0 \rangle = \alpha |00\rangle + \beta |10\rangle$. Applying a CNOT gate to this state would give $CNOT(|\psi\rangle |0 \rangle) = \alpha |00\rangle + \beta |11\rangle$. As you can see, the qubit that corresponds to Bob on the second term is changed from $|0 \rangle$ to $|1 \rangle$. How can this be done if Alice is the one that performs the CNOT and is physically separated from Bob? Doesn't it violate causality?

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Since this variant of the protocol states that Alice has to apply the CNOT gate to both qubits, it implies that the qubits are close enough to have a CNOT applied between them. The problem phrased as it is doesn't say anything about Alice's and Bob's qubits being physically separated.

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