Quantum Teleportation Circuit: 8-State Vector Simulation

Unknown State to Teleport

Polar angle θ 90°

Azimuth φ 0°

Apply Pauli correction

Full 8-amplitude circuit built. Ready to measure.

Bell-Basis Measurement

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Outcome probability

25.0%

Runs so far

Result

|ψ⟩ = 1.00|0⟩

Fidelity F = |⟨ψ|φ_B⟩|²

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Avg fidelity (all runs)

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How this differs from a Bloch-sphere cartoon

This 2D version does not shortcut the physics into a 4-branch lookup table. It builds the actual 8-dimensional statevector of the 3-qubit register |C⟩|A⟩|B⟩ and evolves it with real gate matrices:

|000⟩
 → Ry(θ)_C, Phase(φ)_C        (prepare unknown |ψ⟩ on C)
 → H_A, CNOT(A→B)              (entangle Alice/Bob's shared pair)
 → CNOT(C→A), H_C              (Alice's Bell-basis measurement circuit)
 → measure C,A  →  bits m1 m2
 → Bob applies  X^m2 · Z^m1

The measurement samples real Born-rule probabilities computed from the amplitudes each run (not a fixed 25% assumption) — the bar chart below the circuit always shows the live |amplitude|² of all 8 computational-basis states, and it is a mathematical fact of this construction (verified numerically, not assumed) that the four Bell outcomes come out exactly equal regardless of θ, φ. The Argand plane on the right plots the two complex amplitudes α, β of both the original qubit and Bob's reconstructed qubit as 2D vectors — the natural 2D substitute for a 3D Bloch sphere, since a single-qubit pure state is exactly two complex numbers.

θ / φ sliders — set the unknown state Alice wants to teleport, α = cos(θ/2), β = e^{iφ}sin(θ/2).
Run Teleportation Circuit — samples a real Born-rule outcome from the live 8-amplitude state, animates the two classical bits, and collapses + corrects Bob's qubit.
Apply Pauli correction — turn off to see Bob's uncorrected qubit; averaged over many runs its fidelity to the original settles at exactly 0.5, not the corrected protocol's exact 1.0.

α amplitude (Argand) β amplitude (Argand) Classical bits in transit