DmcsAnchors

Published QPSK bounds reproduced, and how far they sit below the SDP proofs

5/5 passed in 3ms

Test	What it does	Result
test_ghorai_curve	The Ghorai et al. PRX 9, 021059 (2019) QPSK curve as replotted in Fig. 9 of Lin, Upadhyaya & Lutkenhaus, PRX 9, 041064 (2019): qkd tracks the digitised curve to better than 0.5% and dies at 74.1 km against 73.6.	✅ pass
test_psk_distance	Denys et al. Fig. 3 left at $\alpha =0.4$, $\xi =0.01$, $\beta =0.95$: the M = 4, 5, 6 rates are 0.051785, 0.054158, 0.054253 bit/symbol, reaching zero at 26.48, 28.40, 28.48 km, and the M = 6 and M = 32 reaches agree to 2.5 m, as Section 5 states.	✅ pass
test_qpsk_vanishes	Denys et al. Fig. 5 caption at 50 km, $\xi =0.02$, $\beta =0.95$: the best QPSK amplitude, 0.2993, leaves -0.00942 bit/symbol while Gaussian modulation still keys.	✅ pass
test_sdp_gap	A declared miss against the SDP of Lin, Upadhyaya & Lutkenhaus, PRX 9, 041064 (2019) Fig. 9: at $\alpha =0.35$, $\xi =0.005$ this bound reaches 0.80 of it at 0 km and 0.40 at 40 km, and nothing by 40 km at $\xi =0.01$ (not like for like: LUL19 coarse-grains to quadrants, $\beta =0.95$ assumes soft information).	✅ pass
test_zstar_source	Denys et al. Eq. (Z-PSK) and Fig. 2: 4-PSK at $\alpha =0.35$, $\xi =0.01$ certifies $Z^{\ast }(T)=\sqrt{T}\cdot 0.7146537$ from z_lin = 0.73463916 and w = 0.01997093, matching the SDP of Ghorai et al., PRX 9, 021059 (2019).	✅ pass