Tensor Representation of Spin States

TL;DR

This paper introduces a tensor-based generalization of the Bloch sphere for representing arbitrary spin states, facilitating easier analysis and transformation of spin density matrices.

Contribution

It presents a novel tensor representation of spin states using covariant matrices, extending Bloch sphere concepts to higher spins and complex quantum systems.

Findings

Provides a compact tensor representation for spin density matrices

Enables simple parametrization of coherent spin states

Offers a criterion for anticoherence in quantum polarization

Abstract

We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light.