Details

If the classical bit is set to a 1, then a Pauli X (or NOT) operation is performed on the upper input qubits. If the classical bit is set to a 1, then a Pauli Z (or Phase Flip) operation is additionally performed on that input qubit. At this point, the processed upper input qubit is sent to Bob, who then measures the processed and unprocessed qubits in the Bell basis state by using a CNOT gate followed by a Hadamard (see the Demonstration Measuring Entangled Qubits for more details), yielding two classical bits. The result is that Bob receives two classical bits, and , that match those that Alice sent, and only a single (upper) qubit conveyed those two bits of information.

References:

P. Kaye, R. Laflamme, and M. Mosca, An Introduction to Quantum Computing, New York: Oxford University Press, 2007.

C. Bennett and S. Wiesner, "Communication via One- and Two-Particle Operators on Einstein–Podolsky–Rosen States," Physical Review Letters, 69(20), 1992 pp. 2881–2884.