Repeater lab · REQ-NET-001 · learn 03

Beat the exponential, if your memory can wait.

Photons in fiber are lost exponentially: at 0.2 dB/km, 1000 km leaves one in 10²⁰. A repeater chain cuts the distance into short segments, entangles each one by trial and error, stores the pairs in quantum memories, and joins them with entanglement swapping until one pair spans the whole link. Below, one random run of that protocol plays out; the chart shows the average rate from the tested model (qll/network/repeater_chain.py, ported line by line to docs/js/repeater_core.js and checked against it to 10⁻¹²).

one run of the nested protocol · segments herald, memories wait (colour fades as the pair decays), neighbours swap

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the link

distance

nesting levels (segments)

memory coherence T

swap success P_s

source + detection p_src

elementary pair fraction f₀

BBPSSW purification rounds

on elementary pairs after every swap too

average rate vs distance · the chain against direct transmission and the repeaterless bound

direct (10⁹ pulses/s × p_src × η)PLOB bound, no repeater can beat without memoriesmemory chain (these settings; gap = memories expire)all-photonic chain, 8 photons per arm

at this distance

segments × length

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elementary success per attempt

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mean time to a pair

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chain rate

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direct rate

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teleportation fidelity

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chain beats direct beyond

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elementary pairs spent per delivered pair

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memory needed for a useful chain faster than direct

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best useful setup here (≤ 16 segments, ≤ 2 rounds)

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Model and its limits: elementary pairs heralded at segment midpoints, one attempt per herald round trip (or per microsecond), nested swapping with classical heralds over each new span, Werner pairs that decay toward the useless mixture with the memory time T; the chain is declared stalled when the expected waiting time exceeds 3T. Sampling the protocol exactly (qll/network/repeater_montecarlo.py) shows this closed form overestimates the waiting time by about 4 % with two levels and 8 % with three at P_s = 0.5 (more when swaps are reliable), so it is slightly conservative; see learn 03/19. For Earth to Mars there is no fiber: this is why the thesis routes the link through free-space relays instead (see the Mars simulator).