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Generation of a maximally entangled state using collective optical pumping

verification/C055/attempts/R002/claim_report.md

C055 - The steady-state error caused by residual spin-motion entanglement is found in simulation...

Verdict: partial Location: Supp. Mat. S2 Type / expected artifact: empirical / math / numeric Claim: The steady-state error caused by residual spin-motion entanglement is found in simulation to be almost identical to that introduced by U_x(sqrt(2 p)), so the main-text simulations apply to both error sources. 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:84 (Supp. Mat. S2).

Conclusion

Claim (supp S2): steady-state error from residual spin-motion entanglement is almost identical to that from U_x(sqrt(2p)). Reimplemented both: (A) unitary U_x(eps); (B) state-dependent residual displacement V=exp[(alpha a^dag - alpha a)(x)S_x] on spin(x)truncated oscillator (NFOCK=16, CPTP verified), motion traced out. Calibrated eps and alpha to the SAME operational p (single-event one-flip probability from |dn,dn>, supp l.82-84). Matched-p steady-state errors 1-F: p=0.005 1.57e-2 vs 1.57e-2 (0.5%); 0.01 3.09e-2 vs 3.12e-2 (1.0%); 0.02 6.01e-2 vs 6.13e-2 (2.0%); 0.04 (4.0%); 0.06 (6.1%). Max rel diff 6.1%, <1% at small p. Almost identical, as claimed. Also confirmed paper's eps=sqrt(2p) (operational p_A~0.0099 at eps=sqrt(20.01)). Requires reimplemented motional model + Fock truncation => partial.

Verification details

Executable rerun: run.py exited 0 in 1.083s; log verification/C055/attempts/R002/run.log.

Output excerpt:

NFOCK=16  params Phi=0.7854 gamma=0.6943 theta=2.2494
  check model-A: at eps=sqrt(2p), p=0.01: operational p_A=0.00993
  check model-A: at eps=sqrt(2p), p=0.02: operational p_A=0.01973
 p(target)    eps_A  alpha_B     1-F (U_x)   1-F (spin-mot)   rel.diff
    0.0050   0.1002   0.0503  1.566437e-02     1.574266e-02  4.998e-03
    0.0100   0.1419   0.0714  3.088845e-02     3.119715e-02  9.994e-03
    0.0200   0.2014   0.1021  6.009273e-02     6.129441e-02  2.000e-02
    0.0400   0.2868   0.1476  1.140064e-01     1.185849e-01  4.016e-02
    0.0600   0.3537   0.1852  1.627131e-01     1.725995e-01  6.076e-02
max pointwise relative difference (matched operational p) = 6.076e-02

Supporting files