Manuscript X-Enter@1 · X-Enter.tex · section · 484b71bc

A carried qubit is not a comparison

Retained diagnostic branches and exact decoding › A carried qubit is not a comparison · lines 1228–1253

The retained program

P_{keep} = λ q : Q . let r = new in let b = Enter (r) in ⟨ b, q ⟩

uses two live qubits. Its classical law is surely $b = 0$ , but

Φ_{keep} (τ_{1} (a)) = ∣ 0 ⟩ ⟨ 0 ∣ \otimes τ_{1} (a)

varies. It carries the input as a quantum reference without performing a relational comparison. Its constant bit does not establish selective closure or supply Option B's missing classical reference. The locally bound register name $r$ in this program is not the second classical coefficient required in Hypothesis hyp:reference.

Displayed formulas in this passage

unlabeled · line 1231
$P_{keep} = λ q : Q . let r = new in let b = Enter (r) in ⟨ b, q ⟩$
unlabeled · line 1240
$Φ_{keep} (τ_{1} (a)) = ∣ 0 ⟩ ⟨ 0 ∣ \otimes τ_{1} (a)$