Localized Excitations from Localized Unitary Operators

TL;DR

This paper investigates the properties of localized unitary operators in quantum systems, demonstrating their role in creating localized excitations, modeling quantum quenches, and relating to entanglement and causality in quantum field theory.

Contribution

It provides a detailed analysis of localized unitary operators, contrasting them with non-unitary operators, and connects their properties to entanglement, causality, and holography in quantum physics.

Findings

Localized unitary operators create localized excitations.

Non-unitary operators generally produce non-local excitations.

A causality relation for entanglement entropy is established.

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.