This is not single-hop teleportation. A quantum repeater chain splits a long line into N short entangled segments (Alice–R1, R1–R2, … Rk–Bob), each generated independently and each imperfect (fidelity F₀). Adjacent segments are merged pairwise by an entanglement-swapping measurement at the shared repeater node, doubling reach each round until one end-to-end Alice–Bob pair remains — drawn here as a binary tree collapsing upward.
Werner-state swap composition:
F_out = F1·F2 + (1-F1)(1-F2)/3
repeat log2(N) rounds to merge N segments
Each swap can fail (the swap-success slider) and must retry — that cost, plus the multiplicative fidelity formula, is the real trade-off quantum repeaters make. Compare "End-to-end (relay)" against "Direct (no relay)": sending one entangled pair straight across N hops with no intermediate swapping decays exponentially toward a useless 50% (maximally mixed), while the relayed value decays far more gently — this gap is the entire reason repeater networks exist.
- Relay hops — number of segments N = 2^rounds; more hops means more swap rounds and a harder direct comparison.
- Per-segment fidelity — how good each short elementary link is before any swapping.
- Swap success probability — chance a single entanglement-swapping measurement succeeds; failures retry (shown as attempts).
- Link-generation probability — chance a segment's elementary entanglement is heralded successfully per attempt.
This models "Quantum Key Distribution" at network scale: the article's point-to-point QKD link is exactly one of these segments, and a repeater chain is what lets secure quantum communication span distances a single noisy channel could never survive.