• Quantum Internet
  • Also: teleportation of entanglement

Entanglement Swapping

A protocol that creates entanglement between two particles that have never interacted, by performing a joint measurement on two intermediary particles that are each entangled with one of the target particles.

Entanglement swapping is a protocol that generates entanglement between two particles that have never directly interacted. It works by exploiting two pre-existing entangled pairs and a Bell basis measurement on one particle from each pair. After the measurement and classical communication of the result, the two remaining particles become entangled. This is the core mechanism behind quantum repeaters and long-distance quantum networks.

The protocol

Consider four qubits labeled AA, BB, CC, DD. Initially:

  • Qubits AA and BB share a Bell state: ∣Φ+⟩AB=12(∣00⟩+∣11⟩)|\Phi^+\rangle_{AB} = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)
  • Qubits CC and DD share a Bell state: ∣Φ+⟩CD=12(∣00⟩+∣11⟩)|\Phi^+\rangle_{CD} = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)

The combined four-qubit state is:

∣Ψ⟩=∣Φ+⟩AB⊗∣Φ+⟩CD|\Psi\rangle = |\Phi^+\rangle_{AB} \otimes |\Phi^+\rangle_{CD}

Now perform a Bell basis measurement on qubits BB and CC together. This projects BB and CC onto one of the four Bell states. Regardless of which Bell state outcome occurs, qubits AA and DD are left in a Bell state. The specific Bell state of AA and DD depends on the measurement outcome, but a simple Pauli correction (communicated classically) can convert it to any desired Bell state.

The result: AA and DD are now entangled, even though they were never in the same location or interacted with each other.

Why this works

The mathematics relies on the completeness of the Bell basis. The four-qubit state can be rewritten by expanding qubits BB and CC in the Bell basis:

∣Ψ⟩=12(∣Φ+⟩BC∣Φ+⟩AD+∣Φ−⟩BC∣Φ−⟩AD+∣Ψ+⟩BC∣Ψ+⟩AD+∣Ψ−⟩BC∣Ψ−⟩AD)|\Psi\rangle = \frac{1}{2}\left(|\Phi^+\rangle_{BC}|\Phi^+\rangle_{AD} + |\Phi^-\rangle_{BC}|\Phi^-\rangle_{AD} + |\Psi^+\rangle_{BC}|\Psi^+\rangle_{AD} + |\Psi^-\rangle_{BC}|\Psi^-\rangle_{AD}\right)

Measuring BB and CC in the Bell basis collapses AA and DD into the corresponding Bell state. This is a form of quantum teleportation applied to entanglement itself rather than to an arbitrary quantum state.

Application in quantum repeaters

Direct transmission of entangled photons through optical fiber is limited by exponential loss. For fiber at telecom wavelengths, the loss is roughly 0.2 dB/km, meaning that over 100 km about 99% of photons are lost. Entanglement swapping solves this by dividing the long link into shorter segments:

  1. Create entanglement over each short segment (say 50 km each)
  2. Perform entanglement swapping at intermediate nodes
  3. The end nodes share entanglement over the full distance

Combined with entanglement distillation to purify noisy entangled pairs, this forms the basis of a quantum repeater chain. This architecture is essential for building the quantum internet.

Why it matters for learners

Entanglement swapping demonstrates that entanglement is not a direct physical connection but a correlation structure in the quantum state. Two particles can become entangled through measurement alone, with no physical interaction between them. This is conceptually striking and practically essential for any quantum network architecture that operates beyond a single laboratory.

See also