Entanglement Swapping

A Bell measurement can entangle two particles that never interacted, the mechanism behind quantum repeaters.

Entangling the unacquainted

Suppose Alice-Bob share one Bell pair and Bob-Charlie share another, but Alice and Charlie have never interacted. If Bob performs a joint Bell measurement on his two qubits, Alice's and Charlie's qubits become entangled, despite having no common past. This is entanglement swapping: it is teleportation applied to one half of an entangled pair rather than to an independent state.

How it works

Bob's Bell measurement projects his two qubits into a Bell state, and by the structure of teleportation it teleports the entanglement Alice's qubit had with Bob onto Charlie's qubit. The outcome of Bob's measurement tells which of four Bell states Alice and Charlie end up in; a classical message lets them apply a local correction to standardize it. No signal is sent faster than light: the correlation is only usable after the classical result arrives.

import numpy as np
# AB and BC each Bell; Bell-measuring the two B qubits
# leaves A and C in a Bell state (up to a Pauli correction)
print('swap: Bell(AB) + Bell(BC) -> Bell(AC) via Bell measurement on B')

Quantum repeaters

Entanglement swapping is the core of the quantum repeater. Direct transmission of entanglement over long fiber fails because loss grows exponentially with distance. Repeaters divide the link into segments, establish entanglement over each short segment, then swap adjacent segments together to extend the entanglement, combining swapping with distillation to keep fidelity high. This chaining is how entanglement can, in principle, span continental distances.

Broader uses

Beyond repeaters, entanglement swapping builds network topologies where entanglement is routed on demand between arbitrary nodes, underpins device-independent protocols across a network, and enables tests of nonlocality between particles with no shared history. It demonstrates vividly that entanglement is a transferable resource, not a fixed property of a particular pair of particles.