I would define the deep state as the *persisting* state, the system of roots beneath the visible tree. When a new president or prime minister is inaugered, the root system does not change, it persists across elections.

As the deep state expands its powers, individual liberties are necessarily reduced. No single person have the depth of power as a deep state and it is possible that no person controls it - it may run merely on the aggregatw of self-preservation of the individuals it employs