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

TL;DR

This paper introduces a method to detect and analyze nonstabilizerness in quantum states using the information lattice, distinguishing short- and long-range nonstabilizerness through a new witness based on total information.

Contribution

It proposes a novel approach to identify long-range nonstabilizerness via the information lattice and introduces a folding procedure to separate global and local contributions.

Findings

Long-range nonstabilizerness is linked to global correlations in quantum states.

The method distinguishes between short- and long-range nonstabilizerness.

Application to the Potts model shows different nonstabilizerness behaviors in ground states.

Abstract

We study nonstabilizerness on the information lattice, and demonstrate that noninteger local information directly indicates nonstabilizerness. For states with a clear separation of short- and large-scale information, noninteger total information at large scales $\Gamma$ serves as a witness of long-range nonstabilizerness. We propose a folding procedure to separate the global and edge-to-edge contributions to $\Gamma$. As an example we show that the ferromagnetic ground state of the spin-1/2 three-state Potts model has long-range nonstabilizerness originating from global correlations, while the paramagnetic ground state has at most short-range nonstabilizerness.