Soumi Ghosh

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Nonstabilizerness quantifies the departure of a quantum state from a stabilizer state—a state that admits an efficient classical representation via the stabilizer formalism. We show that information lattice provides a straightforward way to witness nonstabilizerness of a given quantum state. In particular, stabilizer states admit only integer values of local information on the information lattice, so  the occurrence of noninteger values provides a natural witness of nonstabilizerness. In localized states, characterized by an information gap separating short- and large- scale information on the information lattice, we further demonstrate that a noninteger total information at large scales Γ 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 Γ=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.

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KTH - Royal Institute of Technology
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Contact: Claudia Artiaco