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Generation of a maximally entangled state using collective optical pumping

verification/C082/attempts/R002/claim_report.md

C082 - Identifying |ee> as the excited subspace and applying the effective-operator formalism in...

Verdict: partial Location: Supp. Mat. S6, Eqs. (S14-S17) Type / expected artifact: math / math Claim: Identifying |ee> as the excited subspace and applying the effective-operator formalism in the drive-(C) dressed basis |chi_0>,|chi_pm> yields the effective Hamiltonian Eq. (S15) and effective jump operators Eq. (S16) with constants C_0 = sqrt(2) J/(-i kappa), C_pm = J/(-/+ Omega_C - i kappa). Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain partial -> partial. Limitations: paper_text_only_reimplementation. Source location(s): source/supp_content.tex:200-239 (Eqs. (S14-S17)).

Conclusion

Reiter-Sorensen reduction (heavy analytic). Verified tractable structure: dressed states chi_0,chi_pm (Eq S14) are orthonormal; under drive-(C) generator they have eigenvalues 0 (chi_0) and +/-Omega_C (chi_pm) -> the denominators -i kappa and -/+Omega_C - i kappa. =sqrt2, =1 -> numerators sqrt2 J and J. No-jump rate out of |ee| =2 kappa -> H_NH imaginary part -i kappa. Hence C_0=sqrt2 J/(-i kappa), C_pm=J/(-/+Omega_C - i kappa) (Eq S17) reproduced. Full S15/S16 operator algebra consistent but not re-derived term-by-term; capped at partial.

Verification details

Derivation excerpt: Per the runner instructions I verify the tractable structural pieces and cap the verdict at partial (paper_text_only_reimplementation); a full line-by-line derivation of every term in S15/S16 is not completed.

Executable rerun: run.py exited 0 in 0.972s; log verification/C082/attempts/R002/run.log.

Output excerpt:

== orthonormality of dressed states ==
  <chi0|chi0> = 1.0000+0.0000j
  <chi+|chi+> = 1.0000+0.0000j
  <chi-|chi-> = 1.0000+0.0000j
== drive-(C) generator (sx x 1 + 1 x sx) eigenvalues on dressed states ==
  <chi0|Vc|chi0> = +0.0000  (=> H_C eigenvalue +0.000 Omega_C)
  <chi+|Vc|chi+> = +2.0000  (=> H_C eigenvalue +1.000 Omega_C)
  <chi-|Vc|chi-> = -2.0000  (=> H_C eigenvalue -1.000 Omega_C)
  note: chi_pm are the +/- eigenstates, chi0 is the 0 eigenstate of Vc
== <ee| S_xe^2 |dressed> (numerators for C constants, in units of J) ==

Supporting files