Memory decay
w(a) = w₀ exp(−a/T)
T is a synthetic two-qubit visibility lifetime, not a measured hardware T₂.
Quantum networks · risk-sensitive decisions
What should a repeater do when entanglement is already ageing?
Build four elementary links, combine them through probabilistic swaps, and decide when an old pair is no longer worth keeping. The experiment exposes why a policy that minimises average waiting can still perform poorly in the tail.
Mechanism
A race between connection and decay.
Each elementary link succeeds randomly. Successful pairs wait in memory while missing links are retried; during that wait their Werner visibility falls. Swapping connects neighbouring intervals but can fail and consume both inputs.
Swap composition
wout = gswap wL wR
A successful swap inherits imperfections from both inputs and the swap operation.
Delivered fidelity
F = (1 + 3w) / 4
A pair is useful here only when its delivered fidelity reaches the selected threshold.
- 1Age existing pairs
- 2Generate uncovered links
- 3Select disjoint swaps
- 4Resolve swap outcomes
- 5Discard by policy
- 6Deliver an end-to-end pair
New swap outputs cannot cascade through a second swap in the same slot. Successful outputs preserve inherited visibility but reset their scheduling age to zero. Candidate boundaries are evaluated in the fixed order 1, 3, 2, making event traces auditable and removing otherwise hidden timing advantages.
Interactive research model
Quantum repeater scheduling lab
Change link success, memory decay, and discard policy to compare swap-as-soon-as-possible with risk-sensitive cutoffs.
This is a synthetic protocol-level teaching model, not hardware calibration, a QKD security proof, or a network-performance promise.
- Completion
- —
- Useful pairs
- —
- Mean latency
- —
- CVaR95 latency
- —
Latency–reliability comparison across policies
Further left means shorter average waiting; higher means more pairs meet the fidelity threshold.
Comparison data
| Scheduling policy | Useful pairs | Mean latency | CVaR95 latency |
|---|
Last twelve slots of one episode
Each mark is an entangled interval still in memory; a is its scheduling age. A swap output keeps inherited visibility but resets age to zero and cannot be swapped again until the next slot.
How to investigate
Change one source of uncertainty at a time.
- Begin at p = 0.20, q = 0.80, and T = 20. Compare the five policies before changing a control.
- Shorten the memory lifetime. Check whether aggressive retention still improves completion but damages the useful-pair probability.
- Raise the fidelity threshold from 0.80 to 0.90. Ask whether the policy ranking changes even when mean latency barely moves.
- Lower generation probability. Inspect CVaR rather than only the mean: rare long waits are where memory ageing accumulates.
Research basis
Selected starting points.
The model is positioned against repeater protocols, cutoff policies, exact latency analysis, and decision-process formulations.
- Briegel et al. (1998), “Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication,” Physical Review Letters.
- Sangouard et al. (2011), “Quantum repeaters based on atomic ensembles and linear optics,” Reviews of Modern Physics.
- Shchukin et al. (2019), “Waiting time in quantum repeaters with probabilistic entanglement swapping,” Physical Review A.
- Iñesta et al. (2023), “Optimal entanglement distribution policies in homogeneous repeater chains with cutoffs,” npj Quantum Information.
- Haldar et al. (2024), “Reducing classical communication costs in multiplexed quantum repeaters using hardware-aware quasi-local policies,” Physical Review Applied.