In superdense coding, a sender (Alice) can send a message consisting of two classical bits using one quantum bit (qubit) to the receiver (Bob). The input to the circuit is one of a pair of qubits entangled in the Bell basis state (the upper qubit). The other qubit from the pair (the lower qubit) is sent unchanged to Bob. After processing the upper qubit in one of four ways, it is sent to Bob, who measures the two qubits, yielding two classical bits. The result is that Bob receives two classical bits, and , that match those that Alice sent, but only a single (upper) qubit conveyed those two bits of information.
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.
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.