Moves an unknown qubit state from q0 to q2 using a Bell pair and two classical bits. The original is destroyed.
q0 holds the message. q1 (Alice) and q2 (Bob) start as |Φ+⟩. Alice applies CX [0,1] and H 0, then MEASURE (0, 1). Those two bits go to Bob over a classical channel.
This circuit uses the deferred-measurement form: after MEASURE, CX [1,2] then CZ [0,2] apply the Pauli corrections on Bob. That is the Nielsen/Chuang and Qiskit layout (X from the Alice bit, Z from the message bit). It is equivalent to classically controlled X then Z, and it is not a mid-circuit if (c[]) Pauli ladder.
How it works
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1
Prepare message
Default |+⟩ on q0: H 0. Variants: |0⟩ (nothing), |1⟩ (X 0), |-⟩ (X 0 then H 0).
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2
Bell pair
H 1; CX [1,2] share entanglement between Alice and Bob.
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3
Alice Bell transform
CX [0,1]; H 0 maps the message into the Bell basis of (q0, q1).
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4
Measure and correct
MEASURE (0, 1). CX [1,2] then CZ [0,2] restore the message on q2.
H 0 H 1 CX [1,2] CX [0,1] H 0 MEASURE (0, 1) CX [1,2] CZ [0,2]
Function form: Teleport("plus")
State. q2 = |+⟩ in every branch. The two bits on (q0, q1) are uniformly random.
Each of 00, 01, 10, 11 on (q0, q1) has probability 1/4. Conditional on any branch, q2 is |+⟩ so H then Z on q2 yields |0⟩.
| Basis | Amplitude | Probability |
|---|---|---|
branch 00 |
q2 = |+⟩ |
|
branch 01 |
q2 = |+⟩ |
|
branch 10 |
q2 = |+⟩ |
|
branch 11 |
q2 = |+⟩ |
Notes
- No faster-than-light signalling: Bob needs the two classical bits.
- No cloning: q0 is measured, so the original state is gone.
- After correction, q2 matches the prepared message in every measurement branch.
Change parameters
The write-up above is for the default circuit. Use this control to generate other variants and load them in the simulator.