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

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.

18 pages, 3 figures

References in corpus (6)

• Universal Quantum Computation with Continuous-Variable Cluster States
• Quantum information transfer from spin to orbital angular momentum of photons
• Experimental demonstration of fractional orbital angular momentum entanglement of two photons
• Quantum Multiplexing with the Orbital Angular Momentum of light
• Periodic and discrete Zak bases
• On the relative quantum entanglement with respect to tensor product structure