Chaos by Magic

TL;DR

This paper investigates the evolution of quantum state magic, specifically Mana and Robustness of Magic, in integrable and chaotic regimes of a higher-spin Ising model, revealing that chaos drives states toward maximal magic, which may relate to spacetime emergence in AdS/CFT.

Contribution

It demonstrates how quantum magic measures evolve differently in chaotic versus integrable regimes, linking magic to the emergence of spacetime in holographic duality.

Findings

In chaotic regimes, Mana increases and saturates at a maximum value.

In integrable regimes, Mana and RoM oscillate periodically.

Magic measures relate to the emergence of spacetime geometry in AdS/CFT.

Abstract

There is a property of a quantum state called magic. It measures how difficult for a classical computer to simulate the state. In this paper, we study magic of states in the integrable and chaotic regimes of the higher-spin generalization of the Ising model through two quantities called "Mana" and "Robustness of Magic" (RoM). We find that in the chaotic regime, Mana increases monotonically in time in the early-time region, and at late times these quantities oscillate around some non-zero value that increases linearly with respect to the system size. Our result also suggests that under chaotic dynamics, any state evolves to a state whose Mana almost saturates the optimal upper bound, i.e., the state becomes "maximally magical." We find that RoM also shows similar behaviors. On the other hand, in the integrable regime, Mana and RoM behave periodically in time in contrast to the chaotic case. In the anti-de Sitter/conformal field theory correspondence (AdS/CFT correspondence), classical spacetime emerges from the chaotic nature of the dual quantum system. Our result suggests that magic of quantum states is strongly involved behind the emergence of spacetime geometry.