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

Proposition: A record is not a residual-state certificate

What destructive clock reading does and does not do › Consumption, nonreturn, and the surviving record · lines 824–840 · proof included or linked

I-B@1#prop:record-residual

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Identical clock record laws do not determine the surviving matter state, even on exactly event-calibrated inputs.

Proof. Choose orthogonal matter vectors $∣ a ⟩, ∣ b ⟩$ . Both inputs

P_{0} \otimes ∣ a ⟩ ⟨ a ∣, P_{0} \otimes ∣ b ⟩ ⟨ b ∣

return the deterministic record $0$ . Their matter residuals are orthogonal. More generally, postcomposing every selective block with either of two different trace-preserving matter channels preserves the clock probabilities while changing the residual instrument.

Displayed formulas in this passage

unlabeled · line 832
$P_{0} \otimes ∣ a ⟩ ⟨ a ∣, P_{0} \otimes ∣ b ⟩ ⟨ b ∣$

Nearby in this section

proposition: Proposition: No universal quantum return
remark: Remark: The quantifier matters
section: Consumption, nonreturn, and the surviving record
proposition: Proposition: Forgetting the record
section: Consumption, nonreturn, and the surviving record