DmcsTrusted

The trusted receiver: its POVM, its four observables, and the distance it buys

6/6 passed in 15801ms

Test	What it does	Result
test_moments_ideal_limit	LL20 Sec. IV B's F_Q, F_P, S_Q and S_P are exactly Hermitian and, at an ideal receiver, within 1e-3 of $q$, $p$, $q^2+1/2$ and $p^2+1/2$ away from the cutoff edge.	✅ pass
test_noisy_complete	At three receiver settings the trusted region operators sum to the identity to 1e-13, each positive semidefinite with 1/m on its diagonal.	✅ pass
test_noisy_ideal_limit	As ${\eta }_d\to 1$ with $v_{el}=0$ the trusted region operator converges on dm_region linearly in $1-{\eta }_d$, a decade per decade.	✅ pass
test_trusted_below_step_one	The certified trusted key stays under its Frank-Wolfe value and under the repeaterless capacity $-{\log }_2(1-{\eta }_d\eta )$ at the transmittance Bob sees.	✅ pass
test_trusted_buys_distance	At ${\eta }_d=0.6$, $v_{el}=0.05$ and $\eta$ from 0.9 to 0.05 the trusted proof certifies key while dm_rate with $v_{el}$ referred to the channel input as $\xi +2v_{el}/({\eta }_d\eta )$ certifies none.	✅ pass
test_trusted_falls_with_loss	The certified trusted key falls monotonically with $\eta$ from 0.9 to 0.05, the dual point reported converged at each.	✅ pass