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Strong empiricalAlgorithmsEntanglement and communication

Superdense coding circuit

An entanglement-assisted communication protocol that encodes two classical bits into one transmitted qubit.

communicationentanglementdense codingQiskit

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Superdense coding complements teleportation by making the communication direction and resource assumptions visible.

Circuit & simulation
00 / 01 / 10 / 11100%
What this takes and returns
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 →

How it works

Superdense coding sends two classical bits using one qubit, given a pre-shared Bell pair 12(00+11)\frac{1}{\sqrt2}(|00\rangle+|11\rangle). To send message m1m2{00,01,10,11}m_1m_2\in\{00,01,10,11\}, Alice applies Zm1Xm2Z^{m_1}X^{m_2} 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 CX\mathrm{CX} then HH to disentangle the pair into a computational basis state that decodes exactly to m1m2m_1m_2 — 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.

Implementation
Native
superdense_coding.py
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 = qc
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.

Declared gaps

Nobody has reviewed this record for gaps yet.

Literature & references
Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states1992 · Charles H. Bennett, Stephen J. Wiesner

Original superdense-coding protocol: encoding two classical bits into one transmitted qubit using a shared entangled pair.

doi.org/10.1103/physrevlett.69.2881
Quantum Computation and Quantum Information: 10th Anniversary Edition2010 · Michael A. Nielsen and Isaac L. Chuang

Standard graduate textbook covering the single- and two-qubit gate definitions, matrix identities, and circuit primitives this record states.

doi.org/10.1017/cbo9780511976667