Alice sends two classical bits by transmitting one qubit of a shared Bell pair.
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
Share |Φ+⟩
H 0; CX [0,1]. q0 is Alice, q1 is Bob.
-
2
Encode 11
X 0 then Z 0. This maps |Φ+⟩ onto |Ψ-⟩ (up to global phase).
-
3
Decode
CX [0,1]; H 0. The two-bit message sits in the Z basis of (q0, q1).
H 0 CX [0,1] X 0 Z 0 CX [0,1] H 0
Function form: Superdense(0b11,0,1)
State. |11⟩ (computational basis)
P(11) = 1. Message bits are (q0, q1) = (1, 1).
| Basis | Amplitude | Probability |
|---|---|---|
|11⟩ |
1 |
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.