Communication

Superdense Coding

Alice sends two classical bits by transmitting one qubit of a shared Bell pair.

Qubits 2 Cost O(1) Default Message 11

Alice and Bob share |Φ+⟩ in advance. Alice encodes a two-bit string on her qubit only: 00 → I, 01 → Z, 10 → X, 11 → XZ. She sends that qubit to Bob. Bob applies CX then H (Bell decode) and reads both qubits in Z.

The default message is 11, so Alice applies X then Z. After Bob decodes, the computational basis on (q0, q1) is 11.

How it works

  1. 1
    Share |Φ+⟩

    H 0; CX [0,1]. q0 is Alice, q1 is Bob.

  2. 2
    Encode 11

    X 0 then Z 0. This maps |Φ+⟩ onto |Ψ-⟩ (up to global phase).

  3. 3
    Decode

    CX [0,1]; H 0. The two-bit message sits in the Z basis of (q0, q1).

Default Qubi (static)
H 0
CX [0,1]
X 0
Z 0
CX [0,1]
H 0

Function form: Superdense(0b11,0,1)

Circuit
q0q1HXZH
Expected result

State. |11⟩ (computational basis)

P(11) = 1. Message bits are (q0, q1) = (1, 1).

BasisAmplitudeProbability
|11⟩ 1
100%

Notes

  • Encoding table: 00 identity, 01 Z, 10 X, 11 X then Z.
  • Without the pre-shared pair, one transmitted qubit cannot carry two independent classical bits.

Change parameters

The write-up above is for the default circuit. Use this control to generate other variants and load them in the simulator.