Quantum Reference Frames on Finite Homogeneous Spaces

TL;DR

This paper develops a framework for quantum reference frames using covariant POVMs on finite homogeneous spaces, connecting to coherent states and perspective-neutral approaches, advancing the understanding of quantum reference systems.

Contribution

It introduces a new operational approach to quantum reference frames on finite homogeneous spaces, generalizing previous models and linking to coherent state constructions.

Findings

Covariant POVMs on finite homogeneous spaces model quantum reference frames.

The canonical covariant projection measure leads to rank-one covariant POVMs.

Connections established with coherent states and perspective-neutral frameworks.

Abstract

We present an operationally motivated treatment of quantum reference frames in the setting that the frame is a covariant positive operator valued measure (POVM) on a finite homogeneous space, generalising the principal homogeneous spaces studied in previous work. We focus on the case that the reference observable is the canonical covariant projection valued measure on the given space, and show that this gives rise to a rank-one covariant POVM on the group, which can be seen as a system of coherent states, thereby making contact with recent work in the perspective-neutral approach to quantum reference frames.