Manuscript Oai280-A@1 · Oai280-A.tex · section · 27038823

Finite schedule containment

Stage 1: three different locality questions › Finite schedule containment · lines 402–424

Let $X$ be a finite set of sites with Hilbert spaces $H_{x}$ , and write

H_{X} = x \in X ⨂ H_{x}, A (Y) = B (x \in Y ⨂ H_{x}) \otimes I_{X ∖ Y} .

At tick $t$ , let $P_{t}$ be a partition of $X$ , and

Φ_{t} = B \in P_{t} ⨂ Φ_{t, B}

be a product of complete CPTP maps on the declared block interfaces. Records and failure outputs are included in those interfaces.

For a terminal region $Y$ at tick $T$ , define

N_{T} (Y) = Y, N_{s} (Y) = ⋃ {B \in P_{s + 1} : B \cap N_{s + 1} (Y) \neq = \emptyset} .

Displayed formulas in this passage

unlabeled · line 406
$H_{X} = x \in X ⨂ H_{x}, A (Y) = B (x \in Y ⨂ H_{x}) \otimes I_{X ∖ Y} .$
unlabeled · line 412
$Φ_{t} = B \in P_{t} ⨂ Φ_{t, B}$
unlabeled · line 419
$N_{T} (Y) = Y, N_{s} (Y) = ⋃ {B \in P_{s + 1} : B \cap N_{s + 1} (Y) \neq = \emptyset} .$