Manuscript Oai283-A@1 · Oai283-A.tex · section · 6fb75895

A definite-order process with the circuit as a link

An explicit nonempty pilot and process-matrix insertion › A definite-order process with the circuit as a link · lines 706–722

Oai283-A@1#eq:comb

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Let all three laboratory inputs and outputs have dimension $d$ . Use the Choi convention of Section sec:model, with plain trace probabilities against local Choi matrices. For a state $ρ$ and a channel $C$ , define

W_{ρ, C} = ρ^{T}_{A_{I}} \otimes J (C)_{A_{O} B_{I}}^{T} \otimes J (id)_{B_{O} C_{I}} \otimes I_{C_{O}} .

The transpose on $J (C)$ is the full transpose on its input-output pair, not a partial transpose.

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Oai283-A@1#eq:comb · line 712
$W_{ρ, C} = ρ^{T}_{A_{I}} \otimes J (C)_{A_{O} B_{I}}^{T} \otimes J (id)_{B_{O} C_{I}} \otimes I_{C_{O}} .$

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proposition: Proposition: Valid finite process insertion
section: A definite-order process with the circuit as a link