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Manuscript En02-A@1 · En02-A-v1.tex · definition · bb1319d5

Definition: Selective pure outputs

Conditional compactness without an LP claim · lines 1817–1832

En02-A@1#def:selective

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Represent a strategy branch by

τ^{S}_{κ} ([ψ]) = P^{S}_{ψ} (κ) ∣ U^{S}_{ψ} (κ)⟩ ⟨ U^{S}_{ψ} (κ)∣ .

At zero probability set $τ^{S}_{κ} = 0$ . Then $τ$ is positive semidefinite, has rank at most one, and

tr τ^{S}_{κ} = P^{S}_{ψ} (κ) .

Displayed formulas in this passage

unlabeled · line 1820
$τ^{S}_{κ} ([ψ]) = P^{S}_{ψ} (κ) ∣ U^{S}_{ψ} (κ)⟩ ⟨ U^{S}_{ψ} (κ)∣ .$
unlabeled · line 1829
$tr τ^{S}_{κ} = P^{S}_{ψ} (κ) .$

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