Generation of accessible sets for a class of quantum spin networks

In this paper, we consider the modeling of dynamical spin network systems. The system Hamiltonian governs the evolution of the network system and shows the structure of how the element systems are coupled. Probes are employed to measure a set of spins of the network. For a variety of applications, the state space model is a useful way to describe the system dynamics. One important task in establishing a state space model is to obtain an accessible set containing all the operators coupled to the measurement operators. We provide analytic results on simplifying the process of generating accessible sets. An example is provided to demonstrate the generation of an accessible set under a certain measurement scheme.