Superdense coding
Superdense coding sends two normal bits by sending just one qubit, as long as the sender and receiver already share an entangled pair of qubits. It is the mirror image of teleportation. It is proven to be the best possible: two bits per qubit is the limit, even with entanglement. It runs cleanly as a two-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 normal bits. But the link between them can carry only one qubit. On its own, that can't work. A qubit's amplitudes can take any value, like a dial. Still, the person who receives it can pull out at most one normal bit per qubit. This limit is called the Holevo bound.
It is worth remembering, because it breaks a popular myth. People say qubits "store endless information." They don't. A qubit is not a bigger bit.
Here is the way around it. Say Alice and Bob shared a Bell pair ahead of time. That is two qubits linked by entanglement, one held by each person. Now the one qubit Alice sends can carry both bits.
How does the protocol work?
Ahead of time, someone makes a Bell pair (with an H gate, then a CX gate). They give one qubit to each person. Later, Alice has her two-bit message. She changes only her own qubit:
- to send
00: do nothing - to send
01: apply X - to send
10: apply Z - to send
11: apply X then Z
These four choices steer the shared two-qubit state into four different Bell states. The four are fully distinct, the way north, south, east and west are. (The math word is orthogonal.) That is the trick. It only works because the pair is entangled.
Alice sends her qubit to Bob. Bob undoes the linking step (CX, then H) and measures both qubits. He reads the two bits directly. Fully distinct states can always be told apart, so decoding is certain.
Keep the count honest. Two qubits moved in total: one ahead of time and one now. So the real win is not "2 bits in 1 qubit" overall. It is that half the sending can happen before the message exists, while the link is idle. Think of mailing a friend half of a torn ticket in advance. Later you only need to send the other half.
What are the honest limits?
Entanglement gets used up. Each two-bit message uses up one Bell pair. And getting that pair to Bob cost a qubit trip of its own. So superdense coding never beats one bit per qubit of total traffic. It only changes when the traffic happens.
Noise hurts early. The two-bits-per-qubit rate assumes a perfect Bell pair and a clean link. As the entanglement gets worse, the rate slides smoothly back toward the normal one bit.
Storage is the real bottleneck. Bob must keep his half of the Bell pair in a stable quantum state until the message comes. Quantum memory that is good enough to make this useful at large scale does not exist yet.
It is not compression. Your data doesn't get smaller. This is a fact about how much a link can carry with the help of entanglement. It is proven by information theory.
What does this look like on real hardware?
Superdense coding was one of the first quantum protocols ever shown in a lab. It was done with entangled particles of light (photons) in 1996. Since then, gains from entanglement have been shown over optical fiber too.
As a circuit it is tiny: two qubits and about six gates. That is well within reach of every current device. It makes a nice quick check of two-qubit gate and readout quality.
A clean run shows entanglement doing real, measurable work. It is one of the few quantum effects you can check in a single afternoon. Run it in the Lab. Then compare how different machine types run the same six gates on the hardware comparison page.