Manuscript I-B@1 · I-B-v1.tex · proposition · 5357688f

Proposition: Forgetting the record

What destructive clock reading does and does not do › Consumption, nonreturn, and the surviving record · lines 846–860 · proof included or linked

I-B@1#prop:forget

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For every input operator,

Tr_{R} M_{C} (Z) = Tr_{C} Z .

This identity is reference preserving.

Proof. Writing $Z = \sum_{j, k} ∣ τ_{j} ⟩ ⟨ τ_{k} ∣ \otimes Z_{j k}$ , both sides equal $\sum_{k} Z_{k k}$ . The same computation retains any reference factor.

Displayed formulas in this passage

unlabeled · line 849
$Tr_{R} M_{C} (Z) = Tr_{C} Z .$

Nearby in this section

proposition: Proposition: No universal quantum return
remark: Remark: The quantifier matters
proposition: Proposition: A record is not a residual-state certificate
section: Consumption, nonreturn, and the surviving record
section: Consumption, nonreturn, and the surviving record