Characterization of an operational quantum resource in a critical many-body system

TL;DR

This paper explores the robustness of magic as a quantum resource in a many-body system, revealing long-range correlations near criticality and how temperature influences quantum versus thermal effects.

Contribution

It introduces the behavior of the robustness of magic in the transverse field XY model, highlighting long-range magic correlations and their scaling near quantum critical points.

Findings

Magic correlations peak near the quantum critical point.

Long-range magic persists over large distances unlike entanglement.

Temperature induces a crossover between quantum and thermal dominance.

Abstract

Quantum many-body systems have been extensively studied from the perspective of quantum technology, and conversely, critical phenomena in such systems have been characterized by operationally relevant resources like entanglement. In this paper, we investigate robustness of magic (RoM), the resource in magic state injection based quantum computation schemes in the context of the transverse field anisotropic XY model. We show that the the factorizable ground state in the symmetry broken configuration is composed of an enormous number of highly magical $H$ states. We find the existence of a point very near the quantum critical point where magic contained explicitly in the correlation between two distant qubits attains a sharp maxima. Unlike bipartite entanglement, this persists over very long distances, capturing the presence of long range correlation near the phase transition. We derive scaling laws and extract corresponding exponents around criticality. Finally, we study the effect of temperature on two-qubit RoM and show that it reveals a crossover between dominance of quantum and thermal fluctuations.