Manuscript XXII-C@1 · XXII-C.tex · definition · b9a05a24

Definition: Valid tripartite qubit process

The frozen process class › Fixed parties, dimensions, and Choi convention · lines 235–260

XXII-C@1#def:process, XXII-C@1#eq:positive, XXII-C@1#eq:normalization, XXII-C@1#eq:probability

A matrix $W \in L (H)$ belongs to $W_{3}$ when

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

A local finite-outcome instrument is a list ${M^{a}_{x_{a} ∣ s_{a}}}_{x_{a}}$ of positive matrices whose sum belongs to $C_{a}$ . Its complete joint outcome law is

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

No definite party ordering or causal-separability decomposition is required in this definition.

Displayed formulas in this passage

XXII-C@1#eq:positive · line 238
$W Tr [W (M_{A} \otimes M_{B} \otimes M_{C})] \geq 0, = 1 for every M_{a} \in C_{a} .$
XXII-C@1#eq:normalization · line 238
$W Tr [W (M_{A} \otimes M_{B} \otimes M_{C})] \geq 0, = 1 for every M_{a} \in C_{a} .$
XXII-C@1#eq:probability · line 250
$P_{W} (x ∣ s) = Tr [W a \in J ⨂ M^{a}_{x_{a} ∣ s_{a}}] .$

Definition: Valid tripartite qubit process

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