Manuscript Psy04-B@1 · Psy04-B-v1.tex · theorem · 62c2b6f0

Theorem: Robust separation of declared families

Complete records and robust score allowances › Complete-law robustness · lines 1621–1657 · proof included or linked

Psy04-B@1#thm:robust, Psy04-B@1#eq:robustgap

Suppose an actual quantum complete law is within total variation $e_{Q}$ of the specified protocol law.

Suppose every actual classical null law is within total variation $e_{C}$ of some complete law whose decoder output satisfies the two-state cut factorization and neutral-score convention. Then

E_{Q} s \geq Q_{score} - e_{Q}, null sup E_{C} s \leq \frac{3}{4} + e_{C} .

A lower separation allowance is

g = \frac{1}{2} + \frac{p v ( 1 - 2 ϵ ) r _{T}}{2 2} - e_{Q} - (\frac{3}{4} + e_{C}) .

It is positive exactly when

p v (1 - 2 ϵ) r_{T} > \frac{1}{2} + 22 (e_{Q} + e_{C}) .

Proof. Apply Lemma lem:tv to the common complete-record score, then subtract the null upper allowance from the quantum lower allowance.

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Psy04-B@1#eq:robustgap · line 1636
$g = \frac{1}{2} + \frac{p v ( 1 - 2 ϵ ) r _{T}}{2 2} - e_{Q} - (\frac{3}{4} + e_{C}) .$
unlabeled · line 1631
$E_{Q} s \geq Q_{score} - e_{Q}, null sup E_{C} s \leq \frac{3}{4} + e_{C} .$
unlabeled · line 1646
$p v (1 - 2 ϵ) r_{T} > \frac{1}{2} + 22 (e_{Q} + e_{C}) .$

Theorem: Robust separation of declared families

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