Generalized Pauli constraints

Sammanfattning

This thesis explores the use of generalized Pauli constraints as a diagnostic tool for analyzing reduced quantum states in open quantum systems. The analysis focuses on an excitonic subsystem of the Fenna–Matthews–Olson (FMO) complex, where environmental interactions are described using the Lindblad formalism. The analysis is based on the reduced density matrix and its eigenvalues, known as natural occupation numbers. The facet residual ∆(t) is used as a quantitative measure to track the evolution of the reduced-state spectra near the Pauli polytope boundary. Using numerical data, the system’s time evolution is analyzed in terms of pinning, quasipinning, and deviation from the pure-state structure. The results show that exact pinning does not occur, whereas quasipinning appears at early times when the spectra approach the boundary of the polytope that is formed by the generalized Pauli constraints. At later times, the spectra gradually evolve towards the interior of the polytope, indicating an increased mixed-state behavior caused by environmental interactions. The results provide a geometric description of the decoherence and open-system behavior in reduced quantum systems, illustrating how generalized Pauli constraints can be used to distinguish between different dynamical regimes during system evolution.