Superdense coding
Superdense coding transmits two classical bits by sending a single qubit, provided sender and receiver already share an entangled pair. It is the mirror image of teleportation, it is provably optimal (two bits per qubit is the ceiling, entanglement included), and it runs cleanly as a 2-qubit demo on any current gate-based machine.
| Task | Best classical | Quantum |
|---|---|---|
| Classical bits recoverable from one transmitted qubit | 1 — the Holevo bound, without shared entanglement | 2 — with a pre-shared Bell pair |
What problem does it solve?
Alice wants to send Bob two classical bits, but the channel between them carries only one qubit. Without help, that is impossible: despite a qubit's continuous amplitudes, a receiver can recover at most one classical bit per qubit — the Holevo bound. This is worth internalising, because it kills the popular myth that qubits "store infinite information". A qubit is not a bigger bit.
The workaround: if Alice and Bob shared a Bell pair beforehand, the one qubit Alice sends now can carry both bits.
How does the protocol work?
Ahead of time, someone creates a Bell pair (H, then CX) and gives one qubit to each party. When Alice's two-bit message exists, she touches only her own qubit:
- send
00: do nothing - send
01: apply X - send
10: apply Z - send
11: apply X then Z
These four local operations steer the joint two-qubit state into four mutually orthogonal Bell states — that is the trick, and it only works because the pair is entangled. Alice sends her qubit; Bob undoes the entangling step (CX, then H) and measures both qubits, reading the two bits directly. Orthogonal states are perfectly distinguishable, so decoding is deterministic.
Keep the bookkeeping honest: two qubits moved in total — one in advance, one now. The win is not "2 bits in 1 qubit" overall; it is that half the transmission can happen before the message exists, over an idle channel.
What are the honest limitations?
Entanglement is a consumable. Each two-bit message burns one Bell pair, and distributing that pair cost a qubit transmission of its own. Superdense coding never beats one bit per qubit of total traffic — it redistributes when the traffic happens.
Noise bites early. The two-bits-per-qubit rate assumes a perfect Bell pair and a clean channel. Degraded entanglement degrades capacity smoothly back toward the classical rate.
Storage is the practical bottleneck. The receiver must hold half a Bell pair coherently until the message arrives — quantum memory good enough to make this useful at scale does not exist yet.
It is not compression. Nothing about your data gets smaller; this is a statement about channel capacity with entanglement assistance, proven as a matter of information theory.
What does this look like on real hardware?
Superdense coding was among the first quantum protocols ever demonstrated — with entangled photons in 1996 — and entanglement-assisted capacity gains have since been shown over optical fibre. As a circuit it is tiny: two qubits, about six gates, well within every current device's abilities, which makes it a pleasant smoke test for two-qubit gate and readout quality.
A clean run demonstrates entanglement doing real, quantifiable work — one of the few quantum effects you can verify in a single afternoon. Run it in the Lab, then compare how different architectures execute the same six gates on the hardware comparison page.