Chaos by Magic

Kavli Affiliate: Masahiro Nozaki

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| Summary:

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.

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