Localized Excitations from Localized Unitary Operators
Allic Sivaramakrishnan
TL;DR
This work develops a local-picture framework in which all physical operations arise from localized Hamiltonian deformations, and shows that localized unitary operators inevitably create localized excitations while local non-unitary operators generally do not. It distinguishes separable from non-separable localized unitaries in quantum field theory, arguing that non-separable excitations conflict with locality and causality, and demonstrates that non-unitary local operators can induce non-local state changes. The paper also analyzes entanglement entropy in excited states, proving a causality constraint and showing that the popular quasi-particle picture applies only to operators with definite conformal dimension, with insights relevant to AdS/CFT and bulk reconstruction. Overall, it clarifies the nuanced relationship between locality, causality, and entanglement in time-dependent quantum systems and holographic dualities, while outlining avenues where non-unitary operators can challenge locality or require careful regularization.
Abstract
Localized unitary operators are basic probes of locality and causality in quantum systems: localized unitary operators create localized excitations in entangled states. Working with an explicit form, we explore the properties of these operators in quantum mechanics and quantum field theory. We show that, unlike unitary operators, local non-unitary operators generically create non-local excitations. We present a local picture for quantum systems in which localized experimentalists can only act through localized Hamiltonian deformations, and therefore localized unitary operators. We demonstrate that localized unitary operators model certain quantum quenches exactly. We show how the Reeh-Schlieder theorem follows intuitively from basic properties of entanglement, non-unitary operators, and the local picture. We show that a recent quasi-particle picture for excited-state entanglement entropy in conformal field theories is not universal for all local operators. We prove a causality relation for entanglement entropy and connect our results to the AdS/CFT correspondence.