Schmidt-mode number as a predictor of multimode repeater speed-up

Determine whether the Schmidt mode number of the two-photon state represents the expected entanglement-generation speed-up of a multimode quantum repeater relative to a single-mode repeater.

Background

The paper introduces the Schmidt mode number as an effective measure of the temporal multimode capacity of the entangled photon-pair source and quantum-memory system. In a simplified model involving heralding on the telecom idler detection time and ideal filtering of the corresponding conditional signal modes after memory storage, the authors show in the Supplementary Information that the speed-up factor equals the Schmidt mode number.

The authors note that ideal conditional-mode filtering is infeasible in practice. Realistic entanglement-distribution rates also depend on the detection time window, SPDC pump power, and repeater swap depth or nesting level. Consequently, it remains unresolved whether the Schmidt mode number provides a quantitatively accurate measure of the practical speed-up achieved by multimode quantum repeaters.