Geometry of pure states of N spin-J system

TL;DR

This paper explores the geometric structure of pure states in an ensemble of N spin-J systems using a generalized Majorana representation, with applications in decoherence-free subspaces.

Contribution

It introduces a novel geometric framework for pure states of N spin-J systems based on Schur-Weyl duality, extending the Majorana representation.

Findings

Provides a geometric interpretation of state transformations

Demonstrates application to decoherence-free subspaces

Simplifies understanding of permutation group actions

Abstract

We present the geometry of pure states of an ensemble of N spin-J systems using a generalisation of the Majorana representation. The approach is based on Schur-Weyl duality that allows for simple interpretation of the state transformation under the action of general linear and permutation groups. We show an exemplary application in theory of decoherence free subspaces and noiseless subsystems.