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Quantum Teleportation Protocol

Advanced quantum

Alice’s state ∣ψ⟩|\psi\rangle is parameterised on the Bloch angles. Stepped playback advances the register through entanglement, Bell measurement, and the classically controlled Xm2/Zm1X^{m_2}/Z^{m_1} corrections; hovering any gate reveals its action in Dirac notation.

12 components · 11 connections · stepped three-qubit protocol

recommended lab 5 of 11

Explain why entanglement and two classical bits are both necessary for teleportation.

Builds on: Bell-State Entanglement Visualizer

predict · then test

Alice completes her Bell measurement but Bob receives no correction bits. What happens to fidelity?

Commit before the explanation appears. This is a prediction, not a quiz score.

governing model
∣ψ⟩=α∣0⟩+β∣1⟩  ⋅  α=cos⁡θ2, β=eiϕsin⁡θ2|\psi\rangle = \alpha|0\rangle + \beta|1\rangle \;\cdot\; \alpha = \cos\tfrac{\theta}{2},\ \beta = e^{i\phi}\sin\tfrac{\theta}{2}
structural inventory
  • 3×3\times qubit trace (ψ,A,B)(\psi,A,B)
  • HH + CNOT preparation
  • Bell-basis measurement
  • X/ZX/Z correction gates
boundaries
  • Bloch θ∈[0,π], ϕ∈[0,2π]\theta\in[0,\pi],\ \phi\in[0,2\pi]
  • 66-step protocol
  • fidelity F=∣⟨ψ∣ψout⟩∣2F=|\langle\psi|\psi_{out}\rangle|^2
diagnosis challenge Fault identity withheld: infer it from the changed outputs first.
causal signal trace paused

Prepare ψ\psi and ancillas The unknown state and two ∣0⟩\lvert 0\rangle ancillas enter on separate rails.

step 1 / 6 Prepare ψ and ancillas

control console

∣ψ⟩=0.000∣0⟩+(0.000 + 0.000i)∣1⟩\lvert\psi\rangle=\htmlData{math-slot=alpha}{\mathtt{0.000}}\lvert0\rangle+\left(\htmlData{math-slot=beta}{\text{0.000 + 0.000i}}\right)\lvert1\rangle

protocol playback

  1. initialize
  2. entangle A↔B
  3. Bell-basis rotation
  4. measure classical bits
  5. apply Pauli corrections
  6. state reconstructed

switchboard · fault injection

test bed · mode=full

Quantum Teleportation Protocol12 components and 11 connections.PSI|ψ⟩A|0⟩B|0⟩HH1HCX1CNOTCX2CNOTHH2HMZ1MZMZ2MZXm2XCXm2Zm1ZCZm1OUT|ψ⟩
Quantum Teleportation Protocol

instrumentation rack

P(0)=0.000P(\htmlData{math-slot=state}{\mathtt{0}})=\htmlData{math-slot=value}{\mathtt{0.000}} P(0)=0.000P(\htmlData{math-slot=state}{\mathtt{0}})=\htmlData{math-slot=value}{\mathtt{0.000}}
teleportation fidelity · F=∣⟨ψ∣ψout⟩∣2F=\lvert\langle\psi\vert\psi_{\mathrm{out}}\rangle\rvert^2
F=—F=\htmlData{math-slot=value}{\text{—}} run the protocol
  • α\alpha
  • β∠φ\beta\angle\varphi
state phasor
diagnostic probe