Superdense coding: send 2 classical bits using 1 qubit + 1 pre-shared entangled pair. A direct corollary of the Bell state structure — each Pauli encodes a distinct message.
Select the 2-bit message Alice wants to send to Bob:
00
Apply: I
|Φ⁺⟩ = (|00⟩+|11⟩)/√2
01
Apply: X
|Ψ⁺⟩ = (|10⟩+|01⟩)/√2
10
Apply: Z
|Φ⁻⟩ = (|00⟩−|11⟩)/√2
11
Apply: iY
|Ψ⁻⟩ = (|10⟩−|01⟩)/√2
DECODED MESSAGE
|Φ⁺⟩ → Bob measures: 00
Alice applies I — Bell state unchanged. Bob performs CNOT then H, reads 00.