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

TL;DR

This paper introduces a two-level control scheme for quantum state creation using entangled equal-probability states, involving superposition-controlled unitary operators and a relation between entanglement and controllable operators.

Contribution

It presents a novel two-level control method for quantum state engineering that links entanglement with the number of controllable unitary operators.

Findings

Established a relation between entanglement and control capacity.

Demonstrated the control scheme with a two-qubit entangled state example.

Proposed a scheme controlling quantum states via superposition and phase manipulation.

Abstract

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.