Sudden death of entanglement, rebirth of magic

TL;DR

This paper explores how local amplitude damping noise can cause the rebirth of quantum magic in certain states even after entanglement is lost, revealing a duality and symmetry between magic and entanglement.

Contribution

It uncovers the phenomenon where local dissipation can restore quantum magic after entanglement disappears, highlighting a duality and broader implications for quantum state manipulation.

Findings

Magic can reappear after entanglement is lost under local amplitude damping.

The magic-entanglement complementarity relation +=1 holds for all n.

Reborn magic can be concentrated onto a single qubit for distillation.

Abstract

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 $\alpha|0^n\rangle+\beta|1^n\rangle$ ($0<\alpha<\beta$) loses its magic at a lower damping strength $\gamma_-$ and regains it at a higher one $\gamma_+$, while entanglement is irreversibly lost at $\gamma_e$. This magic-entanglement complementarity, $\gamma_e+\gamma_+=1$ for every $n$, reflects a system-environment duality of amplitude damping and persists for a broader class of dissipative channels. For small $\alpha$, 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 $|\Phi^+\rangle$ generates magic immediately, while its Bell-state partner $|\Psi^+\rangle$ remains stabilizer. Together, magic and entanglement reveal a symmetry invisible to either alone.