C019 - The singlet fidelity is estimated from measured spin correlators via F(|Psi^->) = (1/4)(1...

Verdict: verified Location: Experiment Type / expected artifact: math / math Claim: The singlet fidelity is estimated from measured spin correlators via F(|Psi^->) = (1/4)(1 - - - ). 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/main.tex:124-125 (Experiment).

Conclusion

Exact identity |Psi-><Psi-|=(1/4)(I-XX-YY-ZZ) verified (sympy); thus F=(1/4)(1---) for any normalized rho. Matches paper exactly.

Verification details

Derivation excerpt: The two-qubit singlet $|\Psi^-\rangle=\frac{1}{\sqrt2}(|\!\uparrow\downarrow\rangle -|\!\downarrow\uparrow\rangle)$ has projector $$|\Psi^-\rangle\langle\Psi^-|=\frac12\begin{pmatrix}0&0&0&0\\0&1&-1&0\\0&-1&1&0\\ 0&0&0&0\end{pmatrix}$$ in the basis $\{\uparrow\uparrow,\uparrow\downarrow,\downarrow\uparrow,\downarrow\downarrow\}$.

Executable rerun: sympy_check.py exited 0 in 0.578s; log verification/C019/attempts/R002/sympy_check.log.

Output excerpt:

projector == (1/4)(I-XX-YY-ZZ): True
F formula == Tr(rho*proj) given Tr(rho)=1: True
difference after Tr=1: 0

Supporting files

• official verdict.json
• attempt verdict.json
• review.md
• sympy_check.py
• sympy_check.log
• derivation.md