Algorithms · Entanglement and communication
Superdense coding circuit
An entanglement-assisted communication protocol that encodes two classical bits into one transmitted qubit.
Strong empiricalUpdated
A small worked example, computed in your browser. It is not a result from this record's papers.
Superdense coding sends two classical bits
2 qubits sharing a Bell pair; Alice sends the 2-bit message 10 to Bob by acting on her qubit alone.
Step 1 of 5 · H
Probability of each outcome after this step
- 0050%
- 0150%
Starts a Bell pair: Alice and Bob each hold one half.
Probability spreads from 1 outcome to 2. All 2 are equally likely.
Completes the Bell pair.
Probability moves: 1 outcome appears that had none, 1 drops to zero, 2 carry probability now. Up: 11 0.0% → 50.0%. Down: 01 50.0% → 0.0%. This is the step that entangles the qubits: from here on no single qubit has a state of its own, only the register as a whole does.
Alice applies X to her own qubit. In this circuit, X alone encodes the message 10 (X sets the first bit, Z would set the second; neither is applied for the second bit here).
Probability leaves all 2 outcomes it was on and appears on 2 entirely different ones — not one outcome is populated both before and after.
Bob receives Alice's qubit and applies CX, the first half of the Bell-basis decode.
Probability moves: 1 outcome appears that had none, 1 drops to zero, 2 carry probability now. Up: 11 0.0% → 50.0%. Down: 01 50.0% → 0.0%. The entanglement comes apart here: each qubit has a state of its own again.
Bob applies H, completing the decode.
Probability gathers from 2 outcomes onto 1. 10 goes from 50.0% to 100.0%.
Readout Measuring both qubits gives 10, the message, recovered from a single qubit sent over the channel because it started out entangled with the qubit Bob already held.
Open in Studio- Steps4
- Wires2
- Qubits2
- Classical bits2
- Shared resourceBell pair
- Papers2
A part this method uses, worked through
This page says Bell pair
— here is a concrete, runnable instance of it.
A Bell pair
2 qubits, preparing (|00⟩ + |11⟩) / √2.
Where it ends up
- 0050%
- 1150%
Measuring both qubits always gives 00 or 11, each about half the time, and never 01 or 10.
Open this part in StudioSuperdense coding complements teleportation by making the communication direction and resource assumptions visible.
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
Superdense coding sends two classical bits using one qubit, given a pre-shared Bell pair . To send message , Alice applies to her half only, mapping the shared state to one of four orthogonal Bell states. She sends her single qubit to Bob, who now holds both halves and applies then to disentangle the pair into a computational basis state that decodes exactly to — the decoding circuit this record checks. Only one physical qubit travels, but the protocol depends on the Bell pair having been distributed beforehand; it does not transmit two arbitrary qubits' worth of quantum information over one qubit, matching the entry's own caveat that a pre-shared entangled resource, not raw channel capacity, is what is being spent.
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
- Qubits
- 2
- Classical bits
- 2
- Shared resource
- Bell pair
- Encoding
- I / X / Z / XZ
- Transmission
- 1 qubit
- Readout
- 2 classical bits
Hon AliceCXon Alice, BobENCon AliceDECon Alice, Bob
Quantum vs classical
Classical baseline
Compare Entanglement and communication with the strongest classical method for the same instance, input budget, and output metric.
Quantum claim
This reference exposes a quantum circuit pattern; it does not imply an application-level speedup without a matched benchmark.
How to compare
Report input loading, circuit depth, repetitions, classical preprocessing, post-processing, and wall-clock time together.
Nobody has reviewed this record for gaps yet.
from qiskit import QuantumCircuit
message = '10'
qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
if message[0] == '1': qc.z(0)
if message[1] == '1': qc.x(0)
qc.cx(0, 1)
qc.h(0)
qc.measure([0, 1], [0, 1])
FINAL_CIRCUIT = qcRelated entries
- Quantum teleportation
Algorithms
- Bell state measurement
Basic circuits
References
- Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states
Charles H. Bennett, Stephen J. Wiesner · 1992
Original superdense-coding protocol: encoding two classical bits into one transmitted qubit using a shared entangled pair.
- Quantum Computation and Quantum Information: 10th Anniversary Edition
Michael A. Nielsen and Isaac L. Chuang · 2010
Standard graduate textbook covering the single- and two-qubit gate definitions, matrix identities, and circuit primitives this record states.