In this work, a generalized analogue to the Pauli spin matrices is presented and investigated. The proposed Hermitian spin matrices exhibit a general symmetry. The generalized spin projection operators are derived and the electrodynamics for hypothetical fermions are explored using the proposed spin matrices. The fermionic quantum Heisenberg model is constructed using the proposed spin matrices and comparative studies against simulation results using the Pauli spin matrices are conducted. Further analysis on key findings as well as discussions on extending the proposed spin matrix framework to describe hypothetical bosonic systems (spin-1) are provided.

The field dynamics of neutral and charged matter (treated as gauge fields) beyond the event horizon of black holes are investigated. As an extension of the work done in Ganesan (2023) [1], the analysis was done using the combined dynamics of the two-dimensional Yang-Mills and Liouville gravity fields beyond the event horizon. The quantum interactions and symmetry breaking mechanisms of the combined two-dimensional fields are discussed. The second part of this paper explores the quantum dynamics occurring at the event horizon. By considering the structure of the event horizon as a Möbius strip (embedded in three-dimensional space), a formulation for the lower bound of the first energy eigenvalue of a quantum particle (electron) at the event horizon is obtained.

Practical entanglement distillation is a critical component in quantum information theory. Entanglement distillation is often utilized for designing quantum computer networks and quantum repeaters. The practical entanglement distillation problem is formulated as a bilevel optimization problem. A fuzzy formulation is introduced to estimate the quantum state (density matrix) from pseudo-likelihood functions (i.e., quantum state tomography). A scale-independent relationship between fuzzy relations in terms of the pseudo-likelihood functions is obtained. The entanglement distillation optimization problem was solved using the combined coupled map lattice and dual annealing approach. Comparative analysis of the results is then conducted against a standard dual annealing algorithmic implementation.