Entanglement of Local Operators and the Butterfly Effect

Abstract

We study the robustness of quantum and classical information to perturbations implemented by local operator insertions. We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture. The sensitivity to initial conditions that we explore is an illuminating manifestation of the butterfly effect in quantum many-body systems. We derive a "membrane theory" in Haar random unitary circuits to compute the mutual information, logarithmic negativity, and reflected entropy in the local operator state by mapping to a classical statistical mechanics problem and find that any local operator insertion delocalizes information as fast as is allowed by causality. Identical behavior is found for conformal field theories admitting holographic duals where the bulk geometry is described by the eternal black hole with a local object situated at the horizon. In contrast to these maximal scramblers, only an $O(1)$ amount of information is found to be delocalized by local operators in integrable systems such as free fermions and Clifford circuits.

v2: Presentation improved, Appendix A revised

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Cited by in corpus (16)

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• Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
• Reflected entropy is not a correlation measure
• Rényi Mutual Information in Quantum Field Theory
• Information Scrambling with Conservation Laws
• Information Scrambling Versus Quantum Revival Through the Lens of Operator Entanglement
• Topological Defects in Floquet Circuits
• Entanglement Dynamics of the Non-Unitary Holographic Channel
• Bridging Entanglement and Magic Resources within Operator Space
• Local Operator Entanglement in Spin Chains
• An Exact Link between Nonlocal Nonstabilizerness and Operator Entanglement
• Volume-law entanglement entropy of typical pure quantum states
• Logarithmic growth of operator entanglement in a clean non-integrable circuit