Angle and angular momentum -- new twist for an old pair

TL;DR

This paper develops a comprehensive quantum framework linking angular momentum and angular variables, enabling optimal measurements and new quantum technology applications involving discrete and continuous variables.

Contribution

It introduces a full quantum analogy between angular momentum and angular variables, including measurement, EPR-like states, and phase-space representation, serving as a template for other observables.

Findings

Established quantum analogy between angular momentum and angular variables

Identified optimal measurement strategies for conjugate variables

Proposed a new testbed for hybrid quantum technologies

Abstract

Reaching ultimate performance of quantum technologies requires the use of detection at quantum limits and access to all resources of the underlying physical system. We establish a full quantum analogy between the pair of angular momentum and exponential angular variable, and the structure of canonically conjugate position and momentum. This includes the notion of optimal simultaneous measurement of the angular momentum and angular variable, the identification of Einstein-Podolsky-Rosen-like variables and states, and finally a phase-space representation of quantum states. Our construction is based on close interconnection of the three concepts and may serve as a template for the treatment of other observables. This theory also provides a new testbed for implementation of quantum technologies combining discrete and continuous quantum variables.