Disentanglement induced by combined effects of polarization mode dispersion and polarization-dependent loss in optical fibers

To build long-range quantum networks based on fiber channels, there is a growing demand for a generic method to describe the decoherence of polarization-entangled states in fiber environments. In this paper, we propose a theoretical model that describes the decoherence induced by the combined effects of polarization mode dispersion (PMD) and polarization-dependent loss (PDL). Consider a pair of polarization-entangled photons traveling along different optical paths and passing through PMD and PDL elements in arbitrary order. The density matrix and the concurrence of the output state are expressed in terms of parameters related to the orientation and magnitude of the PMD and PDL vectors. We obtain the upper bound on the remaining entanglement after EPR pairs have traversed the general fiber channels for a specific range of parameters. We show that it is possible to achieve nonlocal compensation of simultaneous PMD and PDL to force the output state restore original entanglement. By comparing the theoretical values of concurrence with the data from previous experiments, we prove the efficiency of the model basically.