Manuscript Psy02-A@1 · Psy02-A.tex · definition · d92ce402

Definition: Preparation allowance for a selected moment

Input, preparation, and measurement budgets › Preparation in a moment-compatible metric · lines 1306–1326

Psy02-A@1#def:preparation, Psy02-A@1#eq:prep-allowance

A preparation allowance $p_{j}$ certifies

ϵ \norm Φ (v_{j})_{σ, 2} \leq ϵ \norm Φ (v_{j})_{ρ, 2} + p_{j} .

One sufficient construction uses common purifications $Ψ_{ρ}, Ψ_{σ}$ and

p_{j} = ϵ \norm (Φ (v_{j}) \otimes 1) (Ψ_{σ} - Ψ_{ρ}) .

Displayed formulas in this passage

Psy02-A@1#eq:prep-allowance · line 1309
$ϵ \norm Φ (v_{j})_{σ, 2} \leq ϵ \norm Φ (v_{j})_{ρ, 2} + p_{j} .$
unlabeled · line 1317
$p_{j} = ϵ \norm (Φ (v_{j}) \otimes 1) (Ψ_{σ} - Ψ_{ρ}) .$