C050 - Each error channel is studied by applying the map rho -> (1-p) rho + p M_{i,j} rho M_{i,j...
Verdict: verified
Location: Supp. Mat. S2
Type / expected artifact: math / math
Claim: Each error channel is studied by applying the map rho -> (1-p) rho + p M_{i,j} rho M_{i,j}^dag once per cycle after drive (A).
Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain verified -> verified.
Source location(s): source/supp_content.tex:64-68 (Supp. Mat. S2).
Conclusion
Kraus set {sqrt(1-p)I, sqrt(p)M} with M unitary (C049) gives sum K^dag K = (1-p)I + pI = I for all 16 channels and all p in [0,1]; Choi matrix PSD (CP) and Tr preserved (numerically confirmed). So rho->(1-p)rho + p M rho M^dag is a valid CPTP probabilistic error channel per cycle. Clean mathematical fact -> verified.
Verification details
Executable rerun: run.py exited 0 in 0.58s; log verification/C050/attempts/R002/run.log.
Output excerpt:
sum K^dag K = I for all 16 channels, all p in [0,1]: True
Choi matrix PSD (completely positive) for all p in [0,1]: True
Tr(E(rho)) = Tr(rho) (trace-preserving, numeric): True
E(rho) Hermitian PSD unit-trace for random rho: True
VERDICT_OK: True
Conclusion: Kraus set {sqrt(1-p)I, sqrt(p)M} with M unitary satisfies
sum K^dag K = (1-p)I + pI = I, so the map is CPTP for 0<=p<=1.