Manuscript Hawk05-A@1 · Hawk05-A.tex · section · 449f85bb
Four stages, with the output type fixed
The corrected four-stage narrative and analogies › Four stages, with the output type fixed · lines 1732–1768
stage. A complete isometry prepares an accessible factor and complete residual. If a separately proved comparison makes the accessible channel nearly replacement, recovery has the lower bound in Proposition prop:featureless. In the conserving schedule, is initially near one, so quantum recovery error and complete leakage are both near . Destructive Enter replaces a returned quantum carrier by a classical outcome and enlarges the complete complement by its measurement environment.
peak. In the pure-input flagged schedule, the quantum radiation entropy peaks at . This is a schedule-dependent turnover, not a universal Page time. Recovery error and leakage are not maximal at that cut. More generally, an entropy peak does not establish that recovery is about to begin, by Theorem thm:histories.
stage. Further coherent transfer can reduce complete leakage and enable recovery. This is certified by the channel, not by the entropy slope. For a pure unreferenced input in the flagged schedule, decreases as approaches zero. For a referenced input, the radiation marginal need not become pure. If the returned output is instead only an append-only classical record, its Shannon entropy does not decrease and its whole-code recovery obstruction remains.
stage. A certified quantum endpoint with constant complete complement admits a deterministic reference-preserving decoder. A mixed input-independent syndrome may remain. Terminal Enter plus drop consumes the named residual interface without changing the earlier accessible channel. It does not turn classical records into quantum radiation or prove an energetic explosion. If all returned carriers are classical, exact whole-code recovery is impossible for .