Manuscript VIII-A@3 · VIII-A-v3.tex · corollary · 2398a747

Corollary: Robust residual distinction

Matter interfaces and the observation boundary › Complete instrument agreement versus record agreement · lines 463–476 · proof included or linked

VIII-A@3#A:cor:residual-robust

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If implementations of the two outputs in A:thm:residual have trace-distance errors at most $ε_{f}$ and $ε_{c}$ , their mutual trace distance is at least

\frac{1}{2} - ε_{f} - ε_{c} .

Proof. Apply the triangle inequality through the two ideal outputs.

Displayed formulas in this passage

unlabeled · line 469
$\frac{1}{2} - ε_{f} - ε_{c} .$

Nearby in this section

section: Complete instrument agreement versus record agreement
proposition: Proposition: Instrument-level observation criterion
theorem: Theorem: Residual obstruction with an identity coarse instrument
section: Complete instrument agreement versus record agreement
section: Complete instrument agreement versus record agreement