Stochastic decoherence induced by polarization mode dispersion

We address the propagation of entanglement in fibers and investigate the decoherence of polarization-entangled photon pairs caused by polarization mode dispersion (PMD). We devise a decoherence model starting from the statistical properties of polarization mode dispersion and obtain the density matrix describing initially maximally entangled states at any time. Using these results, we derive how decoherence depends on the length of the fibers. We calculate the mean concurrence of the entangled states with PMD effects as a function of fiber length, bandwidth, and other parameters in different cases.