Manuscript XXII-F@1 · XXII-F.tex · definition · 67821705

Definition: Frozen one-use process class

The named quantum data › Process matrices and access · lines 235–262

XXII-F@1#def:class, XXII-F@1#eq:validity, XXII-F@1#eq:probabilities, XXII-F@1#eq:family

Let $W_{3}$ consist of matrices $W$ satisfying

W \geq 0, Tr [W (M_{A} \otimes M_{B} \otimes M_{C})] = 1 (M_{a} \in C_{a}) .

A finite local instrument has positive elements $M^{a}_{x_{a} ∣ s_{a}}$ whose sum belongs to $C_{a}$ . Its complete joint law is

P_{W} (x ∣ s) = Tr [W a \in J ⨂ M^{a}_{x_{a} ∣ s_{a}}] .

The family class is

P_{3q} = (W_{3})^{N} .

Its members $W = (W_{e})_{e \in N}$ are separately tested experiment families.

Displayed formulas in this passage

XXII-F@1#eq:validity · line 238
$W \geq 0, Tr [W (M_{A} \otimes M_{B} \otimes M_{C})] = 1 (M_{a} \in C_{a}) .$
XXII-F@1#eq:probabilities · line 247
$P_{W} (x ∣ s) = Tr [W a \in J ⨂ M^{a}_{x_{a} ∣ s_{a}}] .$
XXII-F@1#eq:family · line 256
$P_{3q} = (W_{3})^{N} .$