Parity-deformed $sl(2,R)$, $su(2)$ and $so(3)$ Algebras: a Basis for Quantum Optics and Quantum Communications Applications

• URL: http://arxiv.org/abs/2407.12157v3
• Date: Tue, 20 May 2025 17:25:53 GMT
• Title: Parity-deformed $sl(2,R)$, $su(2)$ and $so(3)$ Algebras: a Basis for Quantum Optics and Quantum Communications Applications
• Authors: W. S. Chung, H. Hassanabadi, L. M. Nieto, S. Zarrinkamar,
• Abstract summary: Two-mode Wigner algebras are considered adding to them a reflection operator.<n>The associated deformed $sl(2, R)$ algebra, $sl_nu (2,R)$ and the deformed $so(3)$ algebra, $so_nu(3)$, are constructed.<n>Due to its potential application in the study of qubit and qutrit systems, the parity-deformed $so_nu(3)$ representation is analyzed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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, $sl_{\nu}(2,R)$ and the deformed $so(3)$ algebra, $so_{\nu}(3)$, 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 $so_{\nu}(3)$ representation is analyzed based on the isomorphy of $so(3)$ and $su(2)$. Related applications are discussed as well.

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