Manuscript Hawk04-B@2 · Hawk04-B.tex · proposition · ba3b0713

Proposition: Recovery certifies subsequent records

Explicit programs and their output ledgers › Direct radiation observation and observation after recovery · lines 898–916 · proof included or linked

Hawk04-B@2#prop:records

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d_{⋄} (D N_{t}, id_{C}) \leq ε,

then every prescribed terminal observation satisfies

d_{⋄} (M_{F} D N_{t}, M_{F}) \leq ε .

The converse for one chosen observation is false.

Proof. The upper bound is CPTP postprocessing contraction. Computational dephasing preserves the computational-basis observation exactly but annihilates off-diagonal matrix units. That observation equality does not imply quantum recovery.

Displayed formulas in this passage

unlabeled · line 901
$d_{⋄} (D N_{t}, id_{C}) \leq ε,$
unlabeled · line 905
$d_{⋄} (M_{F} D N_{t}, M_{F}) \leq ε .$

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section: Direct radiation observation and observation after recovery
section: Direct radiation observation and observation after recovery