Established background and contribution boundary

Finite-dimensional evaporation models have substantial precedent. Avery studies a class encompassing unitary and nonunitary toy evaporation processes Avery. Hayden and Preskill formulate an information-retrieval task under assumptions including unitary, rapidly mixing internal dynamics and extensive access to radiation HaydenPreskill. Neither model is identified with the extractor specified below.

Reference-based exact recovery is part of the established quantum-error-correction framework KnillLaflamme. Channel continuity and information–disturbance relations are developed by Kretschmann, Schlingemann, and Werner KSW. Bény and Oreshkov formulate approximate-correctability conditions and an environmental dual optimization using worst-case entanglement fidelity BenyOreshkov.

Our contribution is the explicit diagnostic comparison, complete signed channel construction, and population-preserving noise counterexample for the declared extraction family. We do not claim a new general information–disturbance principle, a new definition of quantum recovery, or first-in-literature priority for the elementary dephasing and replacement-channel calculations.

The finite channel is restated and proved independently here. The supplied Em03-H-v8 and Em04-A-v2 manuscripts motivate the comparison, but are not formal premises of its proofs. The XY-chain diagnostic identities of Em04-A are not imported into this different excitation code.