The effects of single-quantum states and entangled states in quantum information based on fractional time Schrödinger equation

Fractional time quantum mechanics is a method for the description of time evolution of quantum dynamics based on fractional derivatives. In this research, by applying fractional order quantum mechanics to quantum information, we introduced a new fractional time Schrödinger equation (FTSE) and constructed two models for the simulation of single-quantum states and entangled states under noise. We find that the results obtained from the two models are consistent with existing physical phenomena under the influence of the FTSE. We also prove that these two models are stable for fractional order α.