SdpStates

The four COW' sequences, their overlaps, and the honest monitoring record

4/4 passed in 6ms

Test	What it does	Result
test_gains_law	The eight honest gains follow the threshold click law, dark floors on the vacuum sequence and the decoy's destructive port, while the data gain rises with intensity and its error rate is dark counts alone.	✅ pass
test_gram_overlaps	The four sequences' Gram matrix is symmetric, with $e^{-\mu }$ between sequences differing in both bins, $e^{-\mu /2}$ in one, and least eigenvalue $(1-e^{-\mu /2}{)}^2$.	✅ pass
test_honest_floor	The honest phase error is $1/2-e^{-\mu }(e^x+1)/4$ at monitor mean photon number x, flooring just under $(1-e^{-\mu })/2$ with perfect detectors and rising with dark counts.	✅ pass
test_split_product	The monitoring record and honest phase error depend on transmittance and splitter only through $\eta (1-t_B)$, the data line through the other product.	✅ pass