Qubits and Quantum Gates

Alice and Bob share a state


and 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|1 >+b|0 >, what quantum gate (i.e., unitary operator) should he apply to his qubit:
(a) If Alice’s outcome was 0?
(b) If Alice’s outcome was 1?


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