Information availability versus executable recovery

Hayden–Preskill recovery concerns information retrieval in an idealized unitary, rapidly mixing model with extensive radiation control HP. Constructive decoding, including conjugate-evolution postselection and coherent amplification, is available in specified idealized settings YK. Clifford dynamics admits additional structured recovery procedures YoshidaClifford. These results must be distinguished from the resources of a particular observer.

We separate three questions:

1. Availability: what message information is present in the accessible radiation?

2. Existence: does a recovery channel achieve the requested reference-preserving accuracy?

3. Execution: can a permitted programme realize such a channel within its memory, circuit-access, record, and time budgets?

The separation itself is not claimed to be new. Our contribution is an exact finite example with a quantitatively optimal memory-constrained error, together with a resource ledger for a recognized constructive recovery architecture.

The principal separation is

The middle equality optimizes over all permitted one-live-qubit decoders, not only a chosen circuit.