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

Definition

Quantum-process data and the event carrier › Faithful generated affine representations · lines 312–329

Oai365-A@1#def:representation, Oai365-A@1#eq:faithful, Oai365-A@1#eq:span, Oai365-A@1#eq:generated

For a declared event poset $(E, ⪯)$ , a faithful generated affine representation is $(V, ι, K)$ , where $V$ is finite-dimensional, $ι : E \to V$ is injective, $K$ is closed, pointed, full-dimensional, and convex, and

p ⪯ q V K ⟺ ι (q) - ι (p) \in K, = span {ι (q) - ι (p) : p, q \in E}, = cone {ι (q) - ι (p) : p ⪯ q, p \neq = q} .

The closure and the event carrier are part of the specification.

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Oai365-A@1#eq:faithful · line 318
$p ⪯ q V K ⟺ ι (q) - ι (p) \in K, = span {ι (q) - ι (p) : p, q \in E}, = cone {ι (q) - ι (p) : p ⪯ q, p \neq = q} .$
Oai365-A@1#eq:span · line 318
$p ⪯ q V K ⟺ ι (q) - ι (p) \in K, = span {ι (q) - ι (p) : p, q \in E}, = cone {ι (q) - ι (p) : p ⪯ q, p \neq = q} .$
Oai365-A@1#eq:generated · line 318
$p ⪯ q V K ⟺ ι (q) - ι (p) \in K, = span {ι (q) - ι (p) : p, q \in E}, = cone {ι (q) - ι (p) : p ⪯ q, p \neq = q} .$

Definition

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