Transfer a quantum state using entanglement and classical bits
Can you move an unknown quantum state to a distant qubit without physically sending the qubit, and without knowing what the state is?
Alice has a qubit (q0) in an unknown state that she wants to send to Bob. They share a Bell pair: Alice holds q1 and Bob holds q2. Alice will perform a Bell-basis measurement on her two qubits, get two classical bits, and send them to Bob. Bob then applies a correction to his qubit. After the correction, Bob's qubit is in the exact same state that Alice's qubit started in — and Alice's original is destroyed.
The Bell pair acts like a shared quantum channel. Alice's measurement does not reveal the state — it projects the three-qubit system into one of four branches, each leaving Bob's qubit in a state that differs from the original by a known Pauli operation (I, X, Z, or XZ). The two classical bits tell Bob which branch occurred, so he knows which correction to apply. The original state is destroyed by Alice's measurement, so no cloning occurs. Classical communication is required, so nothing travels faster than light.
Hadamard puts q1 into superposition. This is the first step in creating the entangled pair that Alice and Bob will share. The Bloch sphere for q1 moves to the equator.
CNOT entangles q1 and q2 into a Bell state: . Alice keeps q1, Bob keeps q2. The histogram now shows only 00 and 11 for the pair. Alice's unknown qubit (q0) is still independent.
Alice applies CNOT from her unknown qubit (q0) to her half of the Bell pair (q1). This entangles Alice's state with the shared pair. All three qubits are now part of one joint state.
Hadamard on Alice's original qubit completes the Bell-basis measurement preparation. The three-qubit state now splits into four equally likely branches, each leaving Bob's qubit in a different but predictable state.
Alice measures both her qubits, obtaining two classical bits (b0, b1). This collapses Bob's qubit into one of four states, each related to the original by a known Pauli operation. The measurement results are random, but the correlation with Bob's qubit is exact.
It is tempting to think teleportation sends information faster than light. That is not what happens. Alice's two measurement bits must travel to Bob through an ordinary classical channel, which is limited by the speed of light. Until Bob receives those bits, his qubit looks completely random. The entanglement enables the transfer, but classical communication is still required to complete it.
After the full protocol with corrections, Bob's qubit (q2) reproduces the measurement statistics of Alice's original state. Alice's qubits collapse to definite classical values. The original state on q0 is destroyed — the state was moved, not copied.
This experiment demonstrates the full quantum teleportation protocol from the Quantum Teleportation algorithm lesson. It combines three core ideas: entanglement (the Bell pair acts as a shared resource), measurement (Alice's Bell-basis measurement collapses the joint state), and classical communication (Bob needs Alice's bits to apply the right correction). It also illustrates the no-cloning theorem in action: the original state is destroyed, so at no point do two copies exist.
Read the full lesson →Why does quantum teleportation not violate the no-cloning theorem?
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