Superdense coding
Send two classical bits by transmitting a single qubit — entanglement pays the difference.
The setup
A lone qubit, measured, yields exactly one classical bit — no trick gets more out of it. Yet if Alice and Bob prepared a shared Bell pair yesterday, Alice can send Bob two full bits today while transmitting only her single qubit. That's superdense coding.
The protocol: Alice and Bob each hold half of (|00⟩+|11⟩)/√2. To encode her two-bit message, Alice applies a gate to her qubit alone: nothing for '00', X for '01', Z for '10', both for '11'. These four operations steer the joint state into four perfectly distinguishable Bell states — even though Bob's half never felt a thing.
Decoding
Alice mails her qubit to Bob. Bob now holds both halves and runs the Bell-pair recipe backwards — CNOT, then H — which maps each of the four Bell states onto a distinct pair of definite bits: |00⟩, |01⟩, |10⟩ or |11⟩. One measurement reads out Alice's whole message.
Load the preset and step through: after Alice's X and Z (columns 2–3), the probability display still shows a 50/50 blur — the message is invisible until decoding. After Bob's CNOT + H, the histogram collapses to 100% |11⟩. Edit columns 2–3 to send the other three messages.
The bigger picture
Superdense coding and teleportation are mirror images: teleportation spends one Bell pair plus two classical bits to move one qubit; superdense coding spends one Bell pair plus one qubit to move two classical bits. Entanglement is the currency in both — and it's consumed on use, which is why neither protocol breaks the light-speed limit or creates information from nothing.
This was many physicists' first glimpse (in 1992) that entanglement is a quantifiable resource, like fuel or bandwidth — the idea that now underpins quantum networking.
- ◆One pre-shared Bell pair lets one transmitted qubit carry two classical bits.
- ◆Alice's local X/Z choices select one of four orthogonal Bell states.
- ◆Teleportation and superdense coding are dual protocols; both spend entanglement.