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Generation of a maximally entangled state using collective optical pumping

verification/C063/attempts/R002/claim_report.md

C063 - For a drive (C) Rabi-frequency imbalance Omega_C^{(2)} = Omega_C^{(1)}(1+epsilon) with th...

Verdict: verified Location: Supp. Mat. S3 Type / expected artifact: numeric / math / numeric Claim: For a drive (C) Rabi-frequency imbalance Omega_C^{(2)} = Omega_C^{(1)}(1+epsilon) with theta=3 pi/4, the singlet is repumped with probability p ~= 1.4 epsilon^2 per cycle, so p<<1e-4 requires epsilon<<1e-2. 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:121 (Supp. Mat. S3).

Conclusion

Paper: drive-C imbalance Omega_C^(2)=Omega_C^(1)(1+eps), theta=3pi/4 -> singlet repumped with p~1.4 eps^2/cycle; p<<1e-4 needs eps<<1e-2. Simulation (U_C -> per-ion rotations theta and theta(1+eps), one cycle S_C_imb S_B S_A applied to |Psi->): per-cycle singlet loss is purely quadratic, p/eps^2=1.388 over eps in [0.002,0.05], LSQ fit c=1.386 vs paper 1.4 (~1%). Threshold p<<1e-4 -> eps<<8.5e-3, consistent with eps<<1e-2. Clean match -> verified.

Verification details

Executable rerun: run.py exited 0 in 0.538s; log verification/C063/attempts/R002/run.log.

Output excerpt:

=== C063: per-cycle singlet-loss vs drive-C imbalance eps (theta=3pi/4) ===
       eps    p=1-F(|Psi->)      p/eps^2
     0.000     4.440892e-16          nan
     0.002     5.551642e-06       1.3879
     0.005     3.469743e-05       1.3879
     0.010     1.387849e-04       1.3878
     0.020     5.550625e-04       1.3877
     0.030     1.248602e-03       1.3873
     0.050     3.465772e-03       1.3863
least-squares fit p = c*eps^2 : c = 1.3865

Supporting files