SargLength

The finite key length, Nian et al., Commun. Theor. Phys. 76, 065101 (2024)

7/7 passed in 1309ms

Test	What it does	Result
test_block_ladder	The maximum secure distance rises with the block from 165.25 km at 1e6 to 172.02 km at 1e10, the first two decades buying 5.47 km and the last two 1.31 km, the shape of their figure 2(a).	✅ pass
test_departure_costs	Nian Eq. (6) as printed reports 7.3% to 7.9% more key at zero distance and 5.0 to 6.0 km more reach than Rusca Eq. (A17), after intensity optimisation.	✅ pass
test_domain_binds	v1/s1 reaches the 1/3 cutoff, certified 20.67% at 200 km against the model's 6.20%, only at 206.06 km, 35.7 km past this configuration's last key at 170.41 km.	✅ pass
test_rate_converges	At 50 km bits per conclusive detection rise from 0.1897 at a 1e6 block to 0.3487 at 1e12, short of the infinite-decoy single-photon 0.4816: the residue is the one-decoy inversion's price, not finite size.	✅ pass
test_route_named	sarg_finite refuses a block size, routing to sarg_length, naming both papers it stands on and keeping its retired reason.	✅ pass
test_two_photon_forgone	Eq. (5) and sarg_length carry no two-photon term, forgoing 13.76% of the asymptotic rate at 50 km for want of a counted lower bound on s2.	✅ pass
test_under_the_ceiling	Every finite block sits under the infinite-decoy reach of 187.72 km on the single-photon term, 191.996 km with the two-photon term Eq. (5) drops, the 1e10 block conceding 15.69 km.	✅ pass