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

Even bipartite non-local magic need not cause response

Stabilizer structure and why the proposed implication fails › Even bipartite non-local magic need not cause response · lines 876–895

En04-A@1#eq:NLindicator

Back to manuscript

To make “non-local” precise for the next counterexample, define a faithful pure-state indicator across a fixed bipartition:

D_{NL}^{A : B} (ψ) = U_{A}, U_{B} s pure stabilizer min d_{tr} ((U_{A} \otimes U_{B}) ∣ ψ ⟩ ⟨ ψ ∣ (U_{A} \otimes U_{B})^{†}, ∣ s ⟩ ⟨ s ∣) .

It is zero exactly when the state is locally unitary-equivalent to a pure stabilizer state. We use it only as an indicator: no monotonicity under arbitrary local operations is asserted. Related non-local magic constructions distinguish removable local magic from magic in correlations Cao2024,CaoEtAl2026.

Displayed formulas in this passage

En04-A@1#eq:NLindicator · line 880
$D_{NL}^{A : B} (ψ) = U_{A}, U_{B} s pure stabilizer min d_{tr} ((U_{A} \otimes U_{B}) ∣ ψ ⟩ ⟨ ψ ∣ (U_{A} \otimes U_{B})^{†}, ∣ s ⟩ ⟨ s ∣) .$

Even bipartite non-local magic need not cause response

Displayed formulas in this passage

Nearby in this section