= Solution
This is <superdense coding>. To send the two classical bits $(z,x)$, Alice applies $Z^zX^x$ to her half of the shared <Bell state> $|\beta_{00}\rangle$, producing $|\beta_{zx}\rangle$, and sends that one qubit to Bob. Bob applies $\operatorname{CX}$ followed by $H$ on the first qubit, as in part (i), and measures both qubits in the <computational basis>. The outcome is $zx$ with certainty, so one transmitted qubit communicates two classical bits using the previously shared <quantum entanglement>.
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