A Highly Nondegenerate Photon-Pair Source for Detector-Matched Quantum Key Distribution

Abstract

In a commercial entanglement-distribution system over telecom fibre, the single-photon detectors are the largest part of the hardware cost. In entanglement-based quantum key distribution (QKD), both photons of each pair must be detected. With two telecom photons, each arm needs either an InGaAs single-photon avalanche diode (SPAD) of low efficiency or a superconducting nanowire single-photon detector (SNSPD) with its own cryostat. We study a highly nondegenerate photon-pair source that needs a telecom detector on one arm only. Two periodically poled KTiOPO$_4$ (ppKTP) crystals pumped at 405~nm emit pairs at 548 and 1550~nm. A Si-SPAD with 82\% efficiency detects the 548~nm photon at the source node, and only the 1550~nm photon travels through fibre. A first, unoptimised module in a polarisation-correlated configuration generates about $1.5\times10^6$ pairs/s per mW of pump power. It collects 13\% of the pairs on the 548~nm arm and 23\% on the 1550~nm arm. In an asymptotic BBM92 model, we compare its links with generic $2\times1550$~nm links that use a bright published source at the same pump power. At 50~km, our link with one SNSPD costs about 25\% more per secret bit than the generic link with one SNSPD. With optimistic target values of 52\% collection and twice the brightness, it costs about 40\% as much as the generic link with two SNSPDs. Our link without a cryostat then costs about 70\% less than the generic link with one SNSPD. If every link runs at its own best pump power, the two-SNSPD link is again the cheapest. The source can also serve clock synchronisation and detector calibration, which need only time-correlated pairs. All key rates assume the entangled configuration of the source, which is under development.

The paper asks whether highly nondegenerate photon pairs can reduce detector costs in fibre-based entanglement QKD by keeping a visible photon local and transmitting only its telecom partner. It characterises a compact, 405-nm-pumped, crossed-ppKTP source emitting at 548 and 1550 nm. Singles and coincidence measurements give an inferred generation rate of approximately $1.5\times10^6$ pairs/s/mW; dead-time-corrected heralding efficiencies, divided by detector efficiencies, imply collection efficiencies of 13.5% and 23.0%, respectively. An asymptotic BBM92 rate model includes detector dead time, afterpulsing and accidental coincidences, and compares Si-SPAD/telecom-detector links with published-source-based $2\times1550$-nm configurations. At 50 km and equal 14.5-mW pump power, the measured-source parameters predict about 11 kbit/s with one SNSPD, costing $376/Gbit over two years versus $301/Gbit for the generic one-SNSPD link. A target source with 52% collection on both arms, twice the brightness and improved loop transmission predicts 150 kbit/s and $27/Gbit, versus $66/Gbit for two SNSPDs. Optimising each link’s pump power instead makes the two-SNSPD comparator cheapest, at $15/Gbit versus $23/Gbit for the target source. Crucially, the measured configuration is expected to be separable and cannot generate BBM92 key: all key rates assume an entangled Sagnac configuration still under development. Other stated limitations include unverified simultaneous brightness and collection targets, residual afterpulsing, approximate component prices, omitted finite-key effects and fibre dispersion, assumed polarisation compensation, and count-rate-dependent timing jitter. The main rate comparisons also omit a dead-time-attack countermeasure whose estimated penalties are reported separately.