Gravitational back-reaction is magical

TL;DR

This paper explores the relationship between quantum magic, entanglement, and gravitational back-reaction, proposing bounds and conjectures supported by analytical and numerical evidence, with implications for holography and classical simulation complexity.

Contribution

It introduces bounds on non-local magic in quantum systems, conjectures its scaling in conformal field theories, and links it to gravitational back-reaction in holographic duals.

Findings

Non-local magic is bounded by entanglement spectrum flatness.

In CFTs, non-local magic scales linearly with entanglement entropy.

Non-local magic vanishes with no gravitational back-reaction in holographic duals.

Abstract

We study the interplay between magic and entanglement in quantum many-body systems. We show that non-local magic, which is supported by the quantum correlations is lower bounded by the non-flatness of entanglement spectrum and upper bounded by the amount of entanglement in the system. We then argue that a smoothed version of non-local magic bounds the hardness of classical simulations for incompressible states. In conformal field theories, we conjecture that the non-local magic should scale linearly with entanglement entropy but sublinearly when an approximation of the state is allowed. We support the conjectures using both analytical arguments based on unitary distillation and numerical data from an Ising CFT. If the CFT has a holographic dual, then we prove that the non-local magic vanishes if and only if there is no gravitational back-reaction. Furthermore, we show that non-local magic is approximately equal to the rate of change of the minimal surface area in response to the change of cosmic brane tension in the bulk.