Teleportation & Superdense Coding
Two mirror-image protocols built entirely from a shared Bell pair
By the end of this topic you'll be able to
Quantum teleportation, introduced by Bennett, Brassard, Crépeau, Jozsa, Peres and Wootters in 1993, sounds as though it ought to violate no-cloning, but it does not: the protocol transfers an unknown state, destroying the original in the process of transmission, rather than duplicating it.
Alice and Bob begin by pre-sharing one Bell pair. Alice, holding an unknown state |ψ⟩ she wants to send, entangles it with her half of the pair and measures both of her qubits — an act that necessarily destroys her own copy of |ψ⟩, exactly as the no-cloning theorem demands — then sends the two classical bits of her measurement outcome to Bob over an ordinary channel.
Depending on which of the four possible outcomes Alice obtained, Bob applies one of four simple correction gates to his half of the pair, and it becomes exactly |ψ⟩. No particle physically moved from Alice to Bob, but the quantum information genuinely did.
The protocol required both the pre-shared entanglement and the classical channel carrying Alice's two bits — so, no, this does not permit faster-than-light communication; Bob's qubit is useless to him until her classical message actually arrives.
Superdense coding, due to Bennett and Wiesner in 1992, runs a similar setup in the opposite direction: with a pre-shared Bell pair, Alice can send Bob two classical bits of information while physically transmitting only one qubit.
She encodes her chosen 2-bit message as one of four gates applied to her half of the pair, sends that single qubit to Bob, and he recovers the full message by measuring the now-reunited pair jointly in the Bell basis — twice the classical capacity a lone qubit would otherwise carry, made possible entirely by the entanglement shared in advance.
Teleportation and superdense coding are, in a precise sense, mirror images of each other: teleportation spends one shared Bell pair plus 2 classical bits to move 1 qubit of quantum information; superdense coding spends the same shared Bell pair plus 1 transmitted qubit to move 2 classical bits. Neither protocol works without the other's resource in reverse — the entanglement has to be shared in advance, before anyone knows what will be sent.
Try It Yourself
Alice wants to teleport |ψ⟩ = (|0⟩+|1⟩)/√2 to Bob. After her Bell-basis measurement on her two qubits, she gets the outcome corresponding to 'apply nothing needed' (the identity case) and sends '00' to Bob. What does Bob need to do, and why?
- 1In the standard teleportation protocol, Alice's measurement outcome tells Bob exactly one of four possible corrections needed: identity (I), X, Z, or XZ, corresponding to her two classical bits 00, 01, 10, 11 respectively.
- 2Alice sent '00', which corresponds to the identity correction — meaning her measurement outcome indicates Bob's half of the pair has already collapsed into exactly |ψ⟩ with no further gate needed.
- 3Bob applies I (does nothing) to his qubit.
- 4His qubit is now |ψ⟩ = (|0⟩+|1⟩)/√2 — the exact state Alice started with, even though it was destroyed on her end the moment she measured, and no particle carrying |ψ⟩ ever physically traveled between them.
Bob applies the identity (does nothing), and his qubit becomes exactly |ψ⟩ = (|0⟩+|1⟩)/√2 — the classical bits '00' told him which of the four possible corrections his half of the pair needs, and in this case it needed none.
Reference
| Teleportation resources | Transfers 1 qubit of quantum information | |
| Superdense coding resources | Transfers 2 classical bits |
Quick Check
Does quantum teleportation violate the no-cloning theorem?
What does superdense coding require to send 2 classical bits using only 1 transmitted qubit?