JCMS: Witnessing Short- and Long-Range Nonstabilizerness via the Information Lattice

by Soumi Ghosh (KTH Royal Institute of Technology)

Monday 16 Feb 2026, 10:30 → 11:30 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

Nonstabilizerness quantifies the distance of a quantum state from a stabilizer state—a state that admits efficient classical representation via the stabilizer formalism. We show that for any given quantum state the information lattice provides a direct identification of nonstabilizerness as stabilizer states admit only integer values for local information on the information lattice. In localized states, characterized by an information gap separating small- and large- scale information on the information lattice, we further demonstrate that a noninteger total information at large scales $\Gamma$ serves as a witness of long-range nonstabilizerness. Using a folding procedure, we further separate the global and edge-to-edge contributions to this witness. We exemplify our approach using the spin-1/2 three state Potts model and show that its ground state in the ferromagnetic phase has long-range nonstabilizerness originating from global correlations. On the other hand, the ground state in the paramagnetic phase can host at most short-range nonstabilizerness having $\Gamma=0$. This framework using information lattice gives a direct way to witness long-range nonstabilizerness and aids in characterization of quantum states in terms of the scale of their nonstabilizerness.