Magic Without Entanglement: Exact Revivals and Their Fisher Information Origin

Research Overview

This paper establishes a rigorous framework connecting two fundamental quantum resources: magic (nonstabilizerness) and entanglement. While both are essential for quantum information processing, their relationship in many-body systems has remained poorly understood. The authors provide two primary theoretical contributions: a geometric bridge between magic and metrology, and a graph-theoretic construction for generating magic without extensive entanglement.

The Tangent Theorem

The authors prove a 'tangent theorem' showing that at any stabilizer state, the leading-order growth of the second stabilizer Renyi entropy under an arbitrary Hermitian generator is exactly equal to the quantum Fisher information (QFI). This result is significant because it provides a bidirectional bridge: the QFI, which is a well-established metrological measure of state sensitivity, acts as the local susceptibility for magic. This offers a concrete experimental protocol for detecting magic in many-body systems by measuring QFI, bypassing the need for full state tomography.

Forest Theorem and Many-Body Dynamics

The second major contribution is the 'forest theorem,' which applies to commuting Ising dynamics on acyclic graphs (forests). By using a Clifford pruning circuit, the authors map complex many-body dynamics to independent single-qubit rotations. This allows for the exact calculation of magic and entanglement for arbitrary system sizes. Crucially, this construction identifies systems where magic density remains finite while entanglement density vanishes in the thermodynamic limit, providing a clear realization of 'magic without entanglement.'

These findings provide a precise, analytical understanding of how magic and entanglement evolve in quantum simulations. By solving paradigmatic models like the Ising quench and kicked Floquet chains, the authors reveal that these two resources exhibit distinct revival periods and behaviors. The work not only offers a new way to quantify magic through established experimental Fisher information measurements but also provides a controlled reference point for studying how non-commuting perturbations lift these exact revivals, offering deep insights into the stability of quantum resources.