Local approximation of observables and commutator bounds

TL;DR

This paper explores the use of conditional expectations as a generalization of partial trace in quantum systems with infinite-dimensional Hilbert spaces, aiming to establish bounds on observables and their commutators.

Contribution

It introduces a framework for local approximation of observables and derives bounds on their commutators in infinite-dimensional quantum systems.

Findings

Conditional expectations generalize partial trace for infinite-dimensional systems

Bounds on observables' commutators are established

Framework aids in local approximation in quantum systems

Abstract

We discuss conditional expectations that can be used as generalizations of the partial trace for quantum systems with an infinite-dimensional Hilbert space of states.