Qubit subalgebra and tensor product in Weyl algebra of angular momentum system

TL;DR

This paper constructs and analyzes a qubit subalgebra within the Weyl algebra of quantum angular momentum, demonstrating a tensor product structure and proposing an experimental realization with photons.

Contribution

It introduces a method to extract qubit subalgebras from angular momentum systems and proves their tensor product structure, enabling scalable quantum encoding.

Findings

The commutant of the qubit subalgebra is isomorphic to the original algebra.

The tensor product structure between the qubit subalgebra and its commutant is established.

An experimental scheme using orbital angular momentum of photons is proposed.

Abstract

We analyze Weyl algebra of quantum angular momentum system and construct qubit subalgebra out of it. We show that the commutant of this qubit subalgebra is isomorphic to the original algebra and prove the tensor product structure between qubit subalgebra and its commutant. This construction can be iterated to construct arbitrary number of qubit subalgebras from a single quantum system. We show a simple experimental realization of this proposed scheme using orbital angular momentum of single photons. We briefly discuss about construction of qudit subalgbra and generalization to other infinite dimensional systems.