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Fast quantum information scrambling and non-integrability are characteristic of generic many-body systems, thought to underpin a number of relevant problems from thermalization of isolated systems to the black hole information paradox. Our results prove a strict separation between these two concepts. Specifically, out-of-time-order correlators (OTOCs) constitute a probe for Local-Operator Entanglement (LOE). There is strong evidence that an extensive growth of LOE is a faithful dynamical indicator of (spectral) quantum chaos, while OTOC decay corresponds to operator scrambling, often conflated with chaos. I will first overview these two concepts, before showing that rapid OTOC decay is a necessary but not sufficient condition for linear (chaotic) growth of LOE entropy. These results are analytically supported through examples of local-circuit models of many-body dynamics, including both integrable and non-integrable dual-unitary circuits. I will also show that this relation is optimal; showing sufficient conditions under which dual unitary dynamics leads to an equivalence of scrambling and chaos, in terms of a spacetime transfer matrix of the Floquet dynamics. Finally, I will overview an application of these notions of many-body chaos in effecting genuinely quantum protections of quantum machine learning algorithms against adversarial attacks.

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Neil Dowling, Monash University, Australia
Seminar Room 0.03, ETP
Contact: Silvia Pappalardi