Quantum Teleportation
Alice has an unknown qubit |ψ⟩. She wants to send it to Bob. She cannot measure it (would collapse). She cannot clone it (no-cloning theorem). With a shared entangled Bell pair, she can: perform a joint measurement, send 2 classical bits to Bob, and Bob applies a correction. The qubit appears on Bob's end. Alice's copy is destroyed. Bennett, Brassard, Crépeau, Jozsa, Peres, Wootters 1993; experimentally first done by Zeilinger 1997.
Click "step" to begin. We'll teleport a qubit step by step.
how three qubits move information without moving particles
The setup: three qubits.
• q₀ = the unknown state Alice wants to send: |ψ⟩ = α|0⟩ + β|1⟩
• q₁, q₂ = a Bell pair (maximally entangled): |Φ⁺⟩ = (|00⟩ + |11⟩)/√2
Alice holds q₀ and q₁. Bob holds q₂ (he can be light-years away).
The protocol:
1. Alice applies CNOT(q₀, q₁) — entangles her two qubits
2. Alice applies Hadamard to q₀ — puts the joint state in the Bell basis
3. Alice measures q₀ and q₁ in the computational basis, getting two classical bits (00, 01, 10, or 11)
4. Alice sends the two bits to Bob via classical channel
5. Bob applies a correction based on the bits: {00: I, 01: X, 10: Z, 11: XZ}
After step 5, Bob's q₂ is in state α|0⟩ + β|1⟩ — exactly the qubit Alice started with. Alice's q₀ has collapsed to a definite |0⟩ or |1⟩ — the original is destroyed (this is what makes teleportation consistent with no-cloning).
Why this isn't faster-than-light communication: Bob's qubit before the classical bits arrive is in a maximally mixed state — random outcomes if he measures. The information arrives only when the 2 classical bits arrive, and those travel at light speed.
What's "teleported": the quantum state — not the qubit itself. The physical particle that ends up as the copy was already at Bob's lab. What moved was the information about how to set its state. This is the foundation of quantum networking, the quantum internet, and distributed quantum computing.