Tracking control of two qubit entanglement using piecewise time-independent method

The tracking control of quantum correlations between two coupled qubits is analyzed, where only one of the qubits is coupled to a Markovian environment. Such a system is a generalized model that can be used, for example, to study the problem of a nuclear spin coupled to the electron spin exposed to the environment. Using an external control field, we increase the time for which the system remains coherent and entangled. The control field is an external potential applied to the system, which contains two adjustable parameters, the intensity and the phase of the field. Furthermore, we present quantum control protocols with different targets. First, for population control of both qubits, second for the coherence control of both two-level systems, and finally for the control of entanglement. Due to analytical for X states the target function can directly be identified with the entanglement. Furthermore, we have shown that when smaller dissipation rates are considered, the control method generates larger stable entanglement between the qubits. (paper)