Superdense Coding

Superdense Coding

Superdense coding is a foundational quantum communication protocol that is, in a sense, the mirror image of quantum teleportation: it lets a sender transmit two classical bits of information to a receiver by physically sending only a single qubit, provided the two parties pre-share an entangled pair. It is a striking demonstration that entanglement effectively doubles the classical information-carrying capacity of a quantum channel. This Cirq example implements the full protocol. The sender and receiver first share a Bell pair; to encode two classical bits, the sender applies one of four Pauli operations (I, X, Z, or XZ) to their half of the pair, each choice rotating the joint entangled state to a different one of the four orthogonal Bell states. The sender then transmits just that one qubit to the receiver, who performs a Bell-state measurement on the two qubits and unambiguously decodes both original bits. The script randomly chooses the two bits to send, builds the encode-and-decode circuit, simulates it, and verifies that the receiver recovers exactly the bits the sender intended. It is a clear, complete illustration of how shared entanglement turns one qubit into a carrier for two classical bits.

Run it

pip install -r requirements.txt
python superdense_coding.py

Source and license

Imported from examples/superdense_coding.py in quantumlib/Cirq at v1.6.1, under the Apache License 2.0. Original authors: The Cirq Developers. The upstream LICENSE is included alongside this example.