A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
Quantum teleportation is a protocol that transmits an unknown qubit state from one party (Alice) to another (Bob) using a shared entangled pair and two classical bits of communication. Alice performs a Bell-basis measurement on her unknown qubit and her half of the entangled pair, then sends the two-bit outcome to Bob, who applies a corrective Pauli gate to recover the original state. No physical qubit travels between them, no faster-than-light communication occurs, and the original state is destroyed in the process — consistent with the no-cloning theorem.
Quantum teleportation seems paradoxical — transmitting a quantum state without sending a quantum particle — but the protocol is straightforward once you trace through the circuit. The setup requires three qubits: qubit 1 is Alice's unknown state |psi> = alpha|0> + beta|1> that she wants to send, and qubits 2 and 3 form a Bell pair (|00> + |11>)/sqrt(2) shared between Alice (qubit 2) and Bob (qubit 3). Alice holds qubits 1 and 2; Bob holds qubit 3.
Alice performs a Bell measurement on qubits 1 and 2. This is implemented by applying CNOT (control = qubit 1, target = qubit 2) followed by Hadamard on qubit 1, then measuring both in the computational basis. The four possible two-bit outcomes (00, 01, 10, 11) occur with equal probability 1/4 regardless of the input state |psi>. The key fact, which you can verify by writing out the algebra, is that for each outcome, Bob's qubit 3 is in a state related to |psi> by a known Pauli transformation: outcome 00 means Bob has |psi>, outcome 01 means Bob has X|psi>, outcome 10 means Z|psi>, and outcome 11 means XZ|psi>.
Alice sends her two-bit measurement result to Bob over a classical channel. Bob applies the corresponding correction: I, X, Z, or XZ. After correction, Bob's qubit is in exactly the state |psi>, with all amplitude and phase information preserved. The teleportation is complete. Notice that the classical communication is essential — without it, Bob's qubit is in a uniformly random state from his perspective. This is why teleportation does not violate special relativity: the useful information only arrives when the classical bits do, which cannot travel faster than light.
Several features of this protocol are worth emphasizing. First, Alice never learns the state |psi> — the Bell measurement destroys the original and produces only two classical bits. Second, the protocol works for any state, including entangled states (teleporting one half of an entangled pair). Third, the entangled pair is consumed: after the protocol, qubits 2 and 3 are no longer entangled. Teleportation thus consumes one entangled pair plus two classical bits to transmit one qubit of quantum information. This resource accounting is the starting point for quantum Shannon theory, which characterizes the fundamental communication costs of quantum information protocols.