Manuscript VII-E@1 · VII-E.tex · lemma · b713cf3c

Lemma: Continuation identity

Restricted destructive deferred readout · lines 1009–1027 · proof included or linked

VII-E@1#lem:continuation, VII-E@1#eq:continuation

For every channel $Λ : L (H_{B}) \to L (H_{B^{'}})$ ,

Tr_{S} [N_{A} ((id_{S A} \otimes Λ) (V ρ V^{†}))] = (id_{R} \otimes Λ) M_{S} (ρ) .

Proof. A channel acting only on $B$ commutes with restriction over $S$ and with carrier readout. Apply lem:recording-restriction and identify the carrier's diagonal basis with the classical record basis.

Displayed formulas in this passage

VII-E@1#eq:continuation · line 1013
$Tr_{S} [N_{A} ((id_{S A} \otimes Λ) (V ρ V^{†}))] = (id_{R} \otimes Λ) M_{S} (ρ) .$

Nearby in this section

section: Restricted destructive deferred readout
lemma: Lemma: Coherent recording followed by restriction
section: Restricted destructive deferred readout
theorem: Theorem: Restricted destructive deferred readout
remark: Remark: The factor removed in the comparison
section: Restricted destructive deferred readout