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Generation of a maximally entangled state using collective optical pumping

verification/C041/attempts/R002/claim_report.md

C041 - Single-ion decay (B) is modelled by Kraus operators E_0 = |down><up|, E_1 =...

Verdict: verified Location: Supp. Mat. S1 Type / expected artifact: math / math Claim: Single-ion decay (B) is modelled by Kraus operators E_0 = |down>down})|down>up})|up><e|, with the two-ion channel given by the nine maps E_i tensor E_j. 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:13 (Supp. Mat. S1).

Conclusion

E0=|d>d)|d>u)|u><e| match the claim. Symbolic (sympy) sum_k E_k^dag E_k = I_3 for general gamma with p_dn=sin^2 g, p_up=cos^2 g (p_dn+p_up=1), proven equal to the identity. Numeric ||sum E^dag E - I_3|| <= 2.2e-16 over a 51-point gamma grid; the nine two-ion maps E_i (x) E_j are also trace-preserving (||sum - I_9|| <= 6.3e-16). Tolerance 1e-12; satisfied. Exact trace-preservation identity -> verified.

Verification details

Executable rerun: run.py exited 0 in 0.726s; log verification/C041/attempts/R002/run.log.

Output excerpt:

E0 ok: True
E1 ok: True
E2 ok: True
symbolic sum E^dag E =
?1  0  0?
?       ?
?0  1  0?
?       ?
?0  0  1?
equals I_3 symbolically: True

Supporting files