• Quantum Internet

Quantum Teleportation

A protocol that transfers an exact quantum state from one qubit to another using a shared Bell pair and two classical bits, without physically moving the qubit.

Quantum teleportation transfers an unknown quantum state ∣ψ⟩|\psi\rangle from Alice’s qubit to Bob’s qubit without physically sending the qubit and without either party ever knowing the state. The original is destroyed in the process. The protocol requires: one shared entangled Bell pair, two classical bits sent from Alice to Bob, and Bob’s ability to apply a conditional correction.

This is not science fiction teleportation. No matter or energy is transmitted. Only the quantum state moves, and it does so at the speed of the classical communication, which cannot exceed the speed of light.

The details

Resources required:

  • A qubit in the unknown state ∣ψ⟩=α∣0⟩+β∣1⟩|\psi\rangle = \alpha|0\rangle + \beta|1\rangle (Alice’s qubit A)
  • A shared Bell pair ∣Φ+⟩=(∣00⟩+∣11⟩)/2|\Phi^+\rangle = (|00\rangle + |11\rangle)/\sqrt{2} distributed between Alice (qubit B) and Bob (qubit C)

Protocol:

Step 1: Alice has qubits A and B. She applies a CNOT gate with A as control and B as target.

Step 2: Alice applies a Hadamard gate to qubit A.

Step 3: Alice measures both qubits A and B in the computational basis, getting two classical bits (m1,m2)(m_1, m_2).

Step 4: Alice sends m1m_1 and m2m_2 to Bob over a classical channel.

Step 5: Bob applies corrections to qubit C based on what he received:

  • If m2=1m_2 = 1: apply XX gate
  • If m1=1m_1 = 1: apply ZZ gate

After the corrections, Bob’s qubit C is in state ∣ψ⟩=α∣0⟩+β∣1⟩|\psi\rangle = \alpha|0\rangle + \beta|1\rangle. The state has been teleported.

The circuit diagram:

Alice's qubit  |ψ⟩ ─────────●──[H]──[M]─────── m1 ──→ Bob applies Z if m1=1
                              │                │
Alice's half   |Φ+⟩A ───────[⊕]────[M]─────── m2 ──→ Bob applies X if m2=1
                                               │
Bob's half     |Φ+⟩B ─────────────────────[X^m2][Z^m1]── receives |ψ⟩

Why does this work? The three-qubit system before Alice’s measurement is in a state where Bob’s qubit is correlated with Alice’s. When Alice measures, the correlation collapses in a specific way depending on the outcome. The two classical bits tell Bob which of four possible states his qubit is in; the correction gates transform any of those four states back into ∣ψ⟩|\psi\rangle.

The protocol is consistent with the no-cloning theorem: Alice’s original qubit is consumed by the Bell measurement. At no point do two copies of ∣ψ⟩|\psi\rangle exist simultaneously.

Why it matters for learners

Quantum teleportation is the fundamental primitive for quantum networking. Every scheme for distributing quantum states across a network, from QKD to distributed quantum computing, ultimately relies on teleportation or entanglement swapping.

Teleportation also clarifies two foundational concepts:

No-cloning: Teleportation works precisely because it destroys the original. The state is moved, not copied.

Classical communication requirement: The two classical bits are not optional. Without them, Bob has no way to determine which correction to apply, and his qubit is in a mixed state with no useful information. This is why teleportation does not allow faster-than-light communication.

Teleportation has been demonstrated experimentally in many platforms: photons, trapped ions, superconducting circuits, and across fiber links. In 2022, researchers demonstrated teleportation over a deployed fiber network in Fermilab, reaching fidelities above 90%90\%.

Common misconceptions

Misconception 1: Quantum teleportation moves matter or energy. Only the quantum state is transferred. The physical qubits remain in place. Alice’s qubit ends the protocol in a collapsed, definite state; Bob’s qubit ends in the desired state ∣ψ⟩|\psi\rangle. No physical object moved.

Misconception 2: Teleportation allows faster-than-light communication. The two classical bits sent from Alice to Bob are required to complete the protocol. They travel at most at the speed of light. Without these bits, Bob’s qubit is useless. Entanglement alone cannot carry information.

Misconception 3: You need to know the state ∣ψ⟩|\psi\rangle to teleport it. The protocol works even when ∣ψ⟩|\psi\rangle is completely unknown to both Alice and Bob. This is the key advantage: you can teleport a quantum state that has never been measured or described classically. This is precisely what makes it useful for quantum networking.

See also