Controlling dephasing decoherence by periodically performing tracking control and generalized measurement

We propose a method to overcome phase damping decoherence by periodically performing open loop tracking control and generalized measurement. Although it is impossible to stabilize a qubit subject to Markovian dynamics only by open loop coherent control, one can attain a dasiasoftenedpsila control goal with the help of periodical generalized measurement. The dasiasoftenedpsila control objective in our scheme is to keep the state of the controlled qubit to stay near a reference pure state all the time. Two sub-optimal control problems are given in the sense of trace distance and fidelity, respectively, and they are eventually reduced to the choice of a period T.