Control theory concerns with the questions if and how it is possible to drive the behavior of a complex dynamical system. A system is said to be controllable if we can drive it from any initial state to any desired state in finite time. For many complex networks, the precise knowledge of system parameters lacks. But, it is possible to make a conclusion about network controllability by inspecting its structure. Classical theory of structural controllability is based on the Lin’s structural controllability theorem, which gives necessary and sufficient conditions to conclude whether a network is structurally controllable. Due to this fundamental theorem, we may identify a minimum driver vertex set, whose control with independent driving signals is sufficient to make the whole system controllable. I show that Lin’s theorem does not apply to quantum networks, if local operations and classical communication between vertices are allowed. Any quantum network can be modified to be structurally controllable obeying a single driving vertex.
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Siomau, M. Any quantum network is structurally controllable by a single driving signal. Quantum Inf Process 18, 1 (2019). https://doi.org/10.1007/s11128-018-2112-6
- Quantum networks
- Linear quantum dynamics