Manuscript VII-E-ST@1 · VII-E-ST.tex · section · d28d9c5d

A finite model selecting ordered slices

A finite model selecting ordered slices · lines 1618–1643

VII-E-ST@1#eq:phases, VII-E-ST@1#eq:model-branches

Only compact regular portions are used by the operations. The extension of a marking toward the completion is background metadata, not an interaction with $W$ and not a claim that these slices are global Cauchy surfaces.

Let matter be one qubit. Set

P_{j} = ∣ j ⟩ ⟨ j ∣, Q = P_{1} - P_{0}, E_{a} = \frac{1}{2} (I + a η Q), M_{a} = E_{a}^{1/2}, 0 \leq η \leq 1,

and

U_{k, q} = e^{- i ϑ_{k, q} Q}, ϑ_{k, q} = \frac{π q}{8} .

For an active input $g$ ,

Ψ_{Γ_{a} (g) ∣ g} (X) = U_{Γ_{a} (g)} M_{a} X M_{a} U_{Γ_{a} (g)}^{†} .

Displayed formulas in this passage

VII-E-ST@1#eq:phases · line 1632
$U_{k, q} = e^{- i ϑ_{k, q} Q}, ϑ_{k, q} = \frac{π q}{8} .$
VII-E-ST@1#eq:model-branches · line 1638
$Ψ_{Γ_{a} (g) ∣ g} (X) = U_{Γ_{a} (g)} M_{a} X M_{a} U_{Γ_{a} (g)}^{†} .$
unlabeled · line 1626
$P_{j} = ∣ j ⟩ ⟨ j ∣, Q = P_{1} - P_{0}, E_{a} = \frac{1}{2} (I + a η Q), M_{a} = E_{a}^{1/2}, 0 \leq η \leq 1,$

A finite model selecting ordered slices

Displayed formulas in this passage

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