Magic Entropy in Hybrid Spin-Boson Systems

TL;DR

This paper introduces new entropic measures to quantify non-classical magic in hybrid spin-boson systems, demonstrating their effectiveness in detecting phase transitions and dynamic phenomena.

Contribution

It develops hybrid magic entropy measures and a Monte Carlo scheme for practical computation, advancing the analysis of quantum magic in complex systems.

Findings

Detection of superradiant phase transition in the Dicke model

Analysis of magic dynamics in the Jaynes-Cummings model after a quench

Development of a Monte Carlo numerical scheme for many-body systems

Abstract

We introduce entropic measures to quantify non-classical resource in hybrid spin-boson systems. We discuss the stabilizer R\'enyi entropy in the framework of phase space quantisation and define an analogous hybrid magic entropy and a mutual magic entropy that capture the distribution of quantum magic across spin and bosonic subsystems. We use these entropic measures to demonstrate two key phenomena: the detection of the superradiant phase transition in the Dicke model and the dynamics of magic in the Jaynes-Cummings model following a quench. We develop a Monte Carlo numerical scheme to enable practical computation in many-body examples.