Manuscript En04-A@1 · En04-A.tex · corollary · bab77211

Corollary: No unconditional magic-to-leakage implication

Stabilizer structure and why the proposed implication fails › Even bipartite non-local magic need not cause response · lines 999–1015 · proof included or linked

En04-A@1#cor:noimplication

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Under the generic prepared-carrier assumptions, neither

non-Clifford program ⟹ δ_{full} > 0

nor

positive bipartite non-local magic ⟹ δ_{full} > 0

is valid. Conversely, $δ_{full} > 0$ does not imply magic.

Proof. Use Proposition prop:independence and Theorem thm:NLcounterexample.

Displayed formulas in this passage

unlabeled · line 1002
$non-Clifford program ⟹ δ_{full} > 0$
unlabeled · line 1006
$positive bipartite non-local magic ⟹ δ_{full} > 0$

Nearby in this section

section: Even bipartite non-local magic need not cause response
lemma: Lemma: Stabilizer reductions have flat nonzero spectra
section: Even bipartite non-local magic need not cause response
theorem: Theorem: A constant complement can contain non-local magic
section: Even bipartite non-local magic need not cause response