Design of observation for multi-qubit preparation based on equilibrium point analysis

We consider multi-qubit quantum spin systems whose behaviors are represented by a stochastic master equation (SME). For generating pure states in the quantum control systems, we analyze the equilibrium points of the SME with respect to the setting of the measurements. As a result of the discussion, we show that commutative property between measurement matrices and the pure state is significance. Finally, we propose a systematic algorithm to design the observation system in order to make a given pure state to be the equilibrium point of the SME and demonstrate its efficiency with a simple example.