DmcsInformation

Exact constellation mutual information against the Gaussian substitution

3/3 passed in 3ms

Test	What it does	Result
test_info_gaussian	The Gaussian branch returns ${\log }_2(1+\mathrm{SNR})$ exactly with noise variance $2+T\xi$, one vacuum unit for the mode and one for Bob's balanced splitter.	✅ pass
test_info_regression	8-PSK at $\alpha =1$, $T=1$, $\xi =0.01$, $\beta =0.95$ turns a 1.9% information gap (0.99640674 Gaussian against 0.97753325 exact) into a 60% key-rate gap (0.047832 against 0.029903), 2.08% at the optimum $\alpha =0.6805$, while QPSK at $\alpha =0.4$, 0 km differs by 0.043% and at $\alpha =0.35$, 20 km by 0.0016%.	✅ pass
test_info_saturates	The exact information rises monotonically to ${\log }_{2}m$ -- 2 bits for QPSK, 6 for 64-PSK at $\alpha =100$ -- while the Gaussian form passes 13 bits.	✅ pass