Manuscript Hawk03-A@1 · Hawk03-A.tex · definition · 9a109c12

Definition: Structural encoding and prepared slice

Encoded algebras and the no-independent-copy obstruction · lines 694–711

Hawk03-A@1#def:structural

Let

H_{L} = H_{M} \otimes H_{A} \otimes H_{B} .

A structural encoding is an isometry $J : H_{L} \to H_{phys}$ . For a fixed pair vector $∣ β ⟩_{A B}$ , its prepared message slice is the isometry

j_{β} : H_{M} \to H_{phys}, j_{β} ∣ ψ ⟩ = J (∣ ψ ⟩_{M} ∣ β ⟩_{A B}) .

A representation of a logical operator $O$ intertwines if

O J = J O .

Displayed formulas in this passage

unlabeled · line 697
$H_{L} = H_{M} \otimes H_{A} \otimes H_{B} .$
unlabeled · line 703
$j_{β} : H_{M} \to H_{phys}, j_{β} ∣ ψ ⟩ = J (∣ ψ ⟩_{M} ∣ β ⟩_{A B}) .$
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$O J = J O .$