Transmitting 2 classical bits using 1 qubit + shared entanglement
Alice's message (2 bits):
① Entangle |Φ⁺⟩ = (|00⟩+|11⟩)/√2
② Alice applies gate to qubit A
③ Alice sends qubit A to Bob
④ Bob Bell measures both
⑤ Bob reads 2-bit message
Message: 00 | Alice applies: I (identity)
Superdense coding (Bennett & Wiesner 1992): Alice and Bob share a Bell state |Φ⁺⟩ = (|00⟩+|11⟩)/√2.
Alice applies one of {I, X, Z, XZ} to encode 2 bits in her single qubit.
After sending her qubit, Bob performs a Bell measurement (CNOT + Hadamard) to extract both bits.
The 4 Bell states are orthogonal and perfectly distinguishable — quantum teleportation in reverse.
This achieves the Holevo bound: 2 classical bits per qubit when entanglement is pre-shared.