A quantum-repeater node needs both halves of a link ready at the same time before it can swap entanglement onward. With a single memory mode, both sides must succeed on the exact same attempt — astronomically unlikely at low per-attempt probability p. Temporal multiplexing gives each node M independent memory modes attempting in parallel, so only one of M needs to succeed each round:
P(≥1 success in M modes) = 1 − (1 − p)^M
Expected trials to first success ≈ 1 / [1 − (1 − p)^M]
A successfully entangled mode does not wait for free: decoherence erodes its fidelity the whole time it sits in memory, following
F(t) = F₀ · e^(−t / T₂)
So multiplexing is a genuine trade-off, not a free lunch: more modes shrink the average synchronization wait (and raise the swap rate), but a mode that got lucky early may sit idle burning down its fidelity while it waits for its partner side. This sim runs both nodes' memory buffers live — every empty mode (dim, wireframe) rolls the dice each attempt tick; a success lights it up and starts its fidelity clock (brightness fades with elapsed hold time); the instant both nodes have at least one live mode, the oldest pair swaps (flash + a photon pulse crossing the middle), the modes reset to empty, and the readouts update from a running average of real trials — not a closed-form estimate.
- M — memory modes per node. Push it up and watch the average wait time collapse and the swap rate climb.
- p — per-attempt, per-mode success probability of generating one heralded entangled pair (photonic loss + detector efficiency, bundled into one number).
- T₂ — memory coherence time. Shorter T₂ punishes long waits harder — watch average fidelity at swap fall as you push M up but T₂ down.
- Attempt rate — how many entanglement-generation attempts run per second of real time (visualization speed, not physics).
Real repeater hardware (atomic-ensemble, NV-center and rare-earth-ion memories) uses exactly this trick — dozens to hundreds of temporal, spectral or spatial modes — because it is usually far cheaper than improving p or T₂ directly.