Generalized Controllability of Quantum Systems: Beyond the Limitation of Open-loop Controllability

To control a quantum system, not only may an ancillary system be introduced, but unitary operations and quantum projective measurement can also be performed on the quantum system or the resulting composite system. As a quantum system may be "physically" controllable even if the quantum system is not open-loop controllable, it is, therefore, necessary to go beyond the limitation of open-loop controllability for quantum systems. By studying the link between quantum generalized measurement and generalized pure state reachability, we further clarify the rationality of redefining the concept of generalized controllability from a view point of physical operation. It is also demonstrated that applying unitary operations, performing quantum projective measurement and introducing ancillary systems can play important roles in controlling quantum systems. Therefore, instead of adopting the concept of open-loop controllability for quantum systems, we need to define and discuss the concept of generalized controllability from a view point of physical operation. This is in marked contrast to the fact that the "physical" controllability for classical systems can only be discussed in the sense of open- loop control.