Manuscript X-L-ST@1 · X-L-ST.tex · proposition · 20a32a22

Proposition: No universal clock return

Recovery of complete residual-report instruments › Report compatibility is weaker than residual compatibility · lines 1697–1713 · proof included or linked

X-L-ST@1#prop:noreturn

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The destructive channel has no left inverse on the full clock input space.

Proof. With the same surviving input, the distinct clock states

\frac{∣ τ _{0} ⟩ + ∣ τ _{1} ⟩}{2}, \frac{∣ τ _{0} ⟩ - ∣ τ _{1} ⟩}{2}

have identical outputs. No fixed left inverse can recover both.

Displayed formulas in this passage

unlabeled · line 1706
$\frac{∣ τ _{0} ⟩ + ∣ τ _{1} ⟩}{2}, \frac{∣ τ _{0} ⟩ - ∣ τ _{1} ⟩}{2}$

Nearby in this section

proposition: Proposition: Equal records can hide a surviving-state difference
section: Report compatibility is weaker than residual compatibility
proposition: Proposition: No acquisition conclusion from the report definition