Proposition: A sufficient calibration budget

Suppose the common actual tested state ${\rho }_A$ satisfies

and the complete score observable $M_{Aj}$ differs from ${\sigma }_j\otimes {\sigma }_j$ by operator norm at most ${\eta }_{Aj}$. Then a sufficient allowance is

Proof. Let $B_A=(I+M_{Ax}-M_{Ay}+M_{Az})/4$. Then $\Vert B_A-P_2\Vert \le {\sum }_j{\eta }_{Aj}/4$. The Bell projector is an effect, so its expectation changes by at most ${\delta }_A$ under the state comparison. Applying both bounds gives the claim.