Manuscript Oai365-A@1 · Oai365-A.tex · section · a3840e3d

Finite process convention

Quantum-process data and the event carrier › Finite process convention · lines 211–246

Each laboratory $a \in {A, B, C}$ has qubit input and output spaces. For a completely positive map $M$ , use the unnormalized Choi operator

J (M) = i, j = 0 \sum^{1} ∣ i ⟩ ⟨ j ∣ \otimes M (∣ i ⟩ ⟨ j ∣) .

A channel satisfies

J (M) \geq 0, Tr_{out} J (M) = I_{in} .

A tripartite process is a positive operator $W$ on the six-qubit input-output space such that

P_{W} (a, b, c) = Tr [W (J (M_{A}^{a}) \otimes J (M_{B}^{b}) \otimes J (M_{C}^{c}))]

is normalized for every triple of local instruments. We use this explicit Choi convention throughout. In this convention the initial state factor of the comb below is transposed.

This is a finite process-matrix interface of the type introduced in OCB. Nothing in its definition assigns spatial positions.

Let $I$ be countable. The datum consists of the separately tested family $(W_{e})_{e \in I}$ , the declared local access, its complete probability functionals, and the derived strengths below.

Displayed formulas in this passage

unlabeled · line 216
$J (M) = i, j = 0 \sum^{1} ∣ i ⟩ ⟨ j ∣ \otimes M (∣ i ⟩ ⟨ j ∣) .$
unlabeled · line 221
$J (M) \geq 0, Tr_{out} J (M) = I_{in} .$
unlabeled · line 228
$P_{W} (a, b, c) = Tr [W (J (M_{A}^{a}) \otimes J (M_{B}^{b}) \otimes J (M_{C}^{c}))]$