Two-level control over quantum state creation via entangled equal-probability state

We propose the scheme realizing the two-level control over the unitary operators \(U_k\) creating the required quantum state of the system S. These operators are controlled by the superposition state of the auxiliary subsystem R which is governed by two control centers. The first-level control center (main control) creates the equal-probability pure state of R with certain distribution of phase factors that, in turn, govern the power of the second-level control center C that applies the special V-operators to the same subsystem R changing its state and thus controlling the applicability of \(U_k\). In addition, the above phases are responsible for the entanglement in the subsystem R. We find the direct relation between this entanglement and the number of operators \(U_k\) that can be controlled by C. The simple example of a two-level control system governing the creation of entangled state of the two-qubit system S is presented.