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Entangled states of two quantum dots mediated by Majorana fermions

With the assistance of a pair of Majorana fermions, we propose schemes to entangle two quantum dots by Lyapunov control in the charge and spin degrees of freedom. Four different schemes are considered, i.e., the teleportation scheme, the crossed Andreev reflection scheme, the intradot spin flip scheme, and the scheme beyond the intradot spin flip. We demonstrate that the entanglement can be generated by modulating the chemical potential of quantum dots with square pulses, which is easily realized in practice. In contrast to Lyapunov control, the preparation of entangled states by adiabatic passage is also discussed. There are two advantages in the scheme by Lyapunov control, i.e., it is flexible to choose a control Hamiltonian, and the control time is much shorter with respect to the scheme by adiabatic passage. Furthermore, we find that the results are quite different by different adiabatic passages in the scheme beyond the intradot spin flip, which can be understood as an effect of quantum destructive interference.