An autocorrelation is not a quantum recovery channel

A classical probability law $p(\sigma )$ can be embedded diagonally as

This is a convex combination of product states and is therefore separable across every spin partition. Classical spin correlations do not by themselves certify quantum entanglement.

A record-only quantum channel is measure-and-prepare and has the corresponding entanglement-breaking limitation CheungVIIIB,CheungHawk04B. That fact does not prevent a classical spin process from having long temporal correlations. It is a statement about unknown-state quantum recovery, not about the value of (eq:physical-correlation).

Our probability model uses classical trajectory observations. It does not insert a destructive quantum measurement into the heat-bath generator. If an implementation uses Enter for quantum-encoded records, its stated consumption rules remain unchanged; no surviving measured quantum wire is inferred CheungI.