Polarization State Dynamics of Single Photon Pulse Under Stochastic Polarization Mode Dispersion for Optical Fiber Quantum Channels

We investigate the polarization state dynamics of single photon pulse for optical fiber quantum communication channels. On the basis of a birefringence vector model in which amplitude and direction are both stochastic variables, Jones vector is obtained by solving the frequency domain wave equation. The fidelity of output quantum state and degree of polarization of the pulse are also obtained from the density operators. It is shown that the fidelity of quantum state decreases quickly and tends to a stable value along optical fiber, and increases for larger mean fluctuation magnitude of the stochastic fiber birefringence. Degree of polarization is nearly constant for small mean fluctuation magnitude of the birefringence. The fidelity and degree of polarization vary in the same way for Gaussian and rectangular frequency spectrum envelope, while the value of Lorentzian spectrum is smaller.