Parity-deformed sl(2,R), su(2) and so(3) algebras: A basis for quantum optics and quantum communications applications

Abstract

Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed 𝑠𝑙(2, 𝑅) algebra, 𝑠𝑙𝜈(2, 𝑅) and the deformed 𝑠𝑜(3) algebra, 𝑠𝑜𝜈(3), are constructed for the widely used Jordan-Schwinger and Holstein-Primakoff realizations, commenting on various aspects and ingredients of the formalism for both single-mode and two-mode cases. Finally, due to its potential application in the study of qubit and qutrit systems, the parity-deformed 𝑠𝑜𝜈(3) representation is analyzed based on the isomorphy of 𝑠𝑜(3) and 𝑠𝑢(2). Related applications are discussed as well.