= Solution
This is <superdense coding>. To encode $00,01,10,11$, Alice applies respectively $I,X,Z,XZ$ to her half of $|\Phi^+\rangle$. These local <Pauli operators> transform the shared state into the four mutually orthogonal <Bell states> $|\Phi^+\rangle,|\Psi^+\rangle,|\Phi^-\rangle,|\Psi^-\rangle$, up to irrelevant global phases. Alice sends her one qubit to Bob. Bob now holds both qubits and performs a <Bell-basis measurement>, whose outcome identifies Alice's two-bit message with certainty. \b[One transmitted qubit communicates two classical bits because one shared Bell pair was available beforehand.]
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