General bound for any quantum control under decoherence
To realize quantum information technologies, quantum control technology for preparing a desired state plays a key role. However, in realistic situation, the actual performance of those methodologies is severely limited by decoherence. Therefore, the following questions arise; how close can we steer the controlled state under decoherence to the ideal target state? To evaluate this problem, we provide an upper bound of the distance between the two controlled open quantum systems in the presence and absence of decoherence. The bound is straightforward to calculate and can be applied to several types of control methods, as demonstrated via numerical simulation.