  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.
