Entanglement is fragile over distance — a qubit fired down 200 km of fibre almost never arrives. And you can’t just amplify it (no-cloning). The fix is beautiful: build a long entangled link out of short ones, by swapping.
Alice and Bob are too far apart to share a pair directly. So we plant relay stations between them, close enough that each neighbour can share a short Bell pair. Now the relays perform a small miracle: a station holding one qubit from each of its two links measures them together — and in doing so fuses the two short links into one longer one, even though its own qubits are consumed in the act. Chain enough of these and the two far ends, which never touched, end up entangled.
Think of a bucket brigade fighting a fire too far from the river to reach in one throw. No one can hurl water the whole distance — but a line of people, each passing a bucket to the next, delivers it just fine. A quantum repeater chain is that brigade for entanglement: no single hop spans the gap, yet each neighbour shares a short link and hands the connection along until the two far ends are joined.
Three short Bell pairs connect four nodes. Click a glowing repeater to make it perform a Bell measurement — its two links merge into one arc reaching further. Two swaps, and A is entangled with B across the whole span.
Node R holds qubit 2 (entangled with A) and qubit 3 (entangled with B). It runs a Bell measurement on its own two qubits. That measurement projects the far qubits A and B into a Bell state — they become entangled, while R’s qubits collapse and drop out:
It is exactly the teleportation circuit — only here the “unknown state” being teleported is itself half of an entangled pair. Teleport the end of one link onto the start of the next, and the entanglement stretches across both.
“A quantum repeater boosts the signal, like the ones on a phone line.” It can’t. A classical repeater reads and re-amplifies — both forbidden here: measuring destroys the state and no-cloning (chapter 7a) blocks copying it for a louder retransmit.
Instead a quantum repeater never touches the carried state at all. It pre-distributes fresh short pairs and stitches them together by swapping — building a long-distance channel without ever amplifying anything. This is the backbone idea of a future quantum internet.