Introduction and contribution boundary

Occupation transfer, coherence, entanglement, marginal purity, and recovery of an unknown quantum message are different diagnostics. A recovery task must specify both the accessible system and the required quantum output, including its correlations with an external reference.

This paper gives an exact comparison within one declared channel family. Its central separation is operational: a pure accessible marginal can contain no message information, whereas a mixed accessible marginal can support exact referenced recovery. Moreover, two experiments can have identical accessible marginals for a Bell input and nevertheless have different optimal recovery errors.

The framework is established. Exact recovery and error-correction conditions are developed by Knill and Laflamme KnillLaflamme; channel continuity and information–disturbance relations by Kretschmann, Schlingemann, and Werner KSW; and approximate recovery through an environmental fidelity optimization by Bény and Oreshkov BenyOreshkov. Our half-diamond metric is not identified with their fidelity metrics. Concurrence and negativity use the established definitions Wootters,VidalWerner.

Finite-dimensional evaporation benchmarks also have precedent Avery, and Hayden–Preskill recovery depends on its own dynamical and access assumptions HaydenPreskill. Neither construction is identified with the channel below.

The contribution here is the explicit signed channel calculation, its local recovery witnesses, a complete flagged decoder, improved intermediate recovery bounds, and a population-preserving noise comparison. All model-specific arguments are supplied in this source. Related manuscripts and the revision proposal motivate these questions but are not formal premises. No exhaustive novelty or first-in-literature claim is made.

scope. The parameter $\eta$ is an extraction probability, not time. The finite channel supplies no black-hole microstate identification, gravitational factorization, passive Hawking-emission mechanism, backreaction law, island construction, or gravitational Page curve. The continuum appendix concerns only its explicitly declared controlled model.