Manuscript Hawk04-A@1 · Hawk04-A.tex · corollary · 526092ba
Corollary: No many-to-one complete unitary channel
The unitary preservation theorem · lines 387–397 · proof included or linked
Hawk04-A@1#cor:injective
Distinct code states cannot have identical complete outputs under the hypotheses of Theorem thm:global. In particular, a complete replacement channel cannot describe that evolution on a nontrivial code.
Proof. Apply the CPTP left inverse, or use preserved trace distance.