Sudden death of entanglement, rebirth of magic

Local Markovian noise cannot bring entanglement back, but it can bring magic back. Unlike separability, stabilizer membership is not preserved by local channels, allowing dissipation to push states out of the stabilizer polytope as well as in. Under local amplitude damping, the $n$-qubit GHZ family $α|0^n\rangle+β|1^n\rangle$ ($0<α<β$) loses its magic at a lower damping strength $γ_-$ and regains it at a higher one $γ_+$, while entanglement is irreversibly lost at $γ_e$. This magic-entanglement complementarity, $γ_e+γ_+=1$ for every $n$, reflects a system-environment duality of amplitude damping and persists for a broader class of dissipative channels. For small $α$, the reborn magic resides in a fully separable state with all proper marginals stabilizer, yet parity-syndrome extraction concentrates it onto a single qubit for magic-state distillation. Local dissipation further divides pure stabilizer states into magic-generators and magic-insulators: at two qubits, the Bell state $|Φ^+\rangle$ generates magic immediately, while its Bell-state partner $|Ψ^+\rangle$ remains stabilizer. Together, magic and entanglement reveal a symmetry invisible to either alone.

Source: arXiv:2605.22603v1 - http://arxiv.org/abs/2605.22603v1 PDF: https://arxiv.org/pdf/2605.22603v1 Original Link: http://arxiv.org/abs/2605.22603v1