Generation of Accessible Sets in the Dynamical Modeling of Quantum Network Systems

In this article, we consider the dynamical modeling of a class of quantum network systems consisting of qubits, where information extraction is allowed by performing measurement on several selected qubits of the system. For a variety of applications, a state space model is a useful approach to modeling the system dynamics. To construct a state space model for a quantum network system, the major task is to find an accessible set containing all of the operators coupled to the measurement operators. This article focuses on the generation of a proper accessible set for a given system and measurement scheme. We provide analytic results on simplifying the process of generating accessible sets for systems with a time-independent Hamiltonian. Since the order of elements in the accessible set determines the form of state space matrices, guidance is provided to effectively arrange the ordering of elements in the state vector. Defining a system state according to the accessible set, one can develop a state space model with a special pattern inherited from the system structure. As a demonstration, we specifically consider a typical 1-D-chain system with several common measurements and employ the proposed method to determine its accessible set.