Manuscript XVII-A@1 · XVII-A.tex · section · 711d7ee4

The correspondence is declared, not inferred

Boundary data and the declared representation correspondence › The correspondence is declared, not inferred · lines 364–385

XVII-A@1#eq:U, XVII-A@1#eq:NB-restriction

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Define a unitary $U : H_{bulk} \to H_{\partial}$ by

U ∣ m_{1}, \dots, m_{K} ⟩_{bulk} = ∣ m_{1}, \dots, m_{K} ⟩_{\partial} .

Then $U a_{n} U^{†} = b_{n}$ . This occupation-basis correspondence is an additional model input. It is not obtained from any decoder in En02, any packet state in Em03, or any finite readout semantics in I.

The boundary-data interface is

N_{B} (ρ) = (U ρ U^{†})_{A (B)} .

The following proposition verifies that the independently displayed boundary family is the normalizable boundary limit of the displayed bulk family under this declared correspondence.

Displayed formulas in this passage

XVII-A@1#eq:U · line 367
$U ∣ m_{1}, \dots, m_{K} ⟩_{bulk} = ∣ m_{1}, \dots, m_{K} ⟩_{\partial} .$
XVII-A@1#eq:NB-restriction · line 377
$N_{B} (ρ) = (U ρ U^{†})_{A (B)} .$

The correspondence is declared, not inferred

Displayed formulas in this passage

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