# How to implement the generalized-coherent-state POVM via nonadaptive continuous isotropic measurement

## TL;DR

This paper explains how to implement generalized-coherent-state POVMs using nonadaptive continuous isotropic measurements, extending previous results to any finite-dimensional Lie group representation, with detailed mathematical insights.

## Contribution

It provides a detailed mathematical framework for implementing generalized-coherent-state POVMs via nonadaptive continuous isotropic measurements for any finite-dimensional Lie group.

## Key findings

- Extended the implementation method to all finite-dimensional Lie group representations
- Provided detailed mathematical explanations of the concepts involved
- Generalized the approach beyond spin-coherent states

## Abstract

In a recent Letter~[PRL \textbf{121}, 130404 (2018)], it was announced that the spin-coherent-state POVM can be implemented via a nonadaptive continuous isotropic measurement. In this article, the mathematical concepts used to prove this are explained in greater depth. Also provided is the more general result of how to implement a generalized-coherent-state POVM for any finite-dimensional unitary representation of a Lie group.