Local filtering operations on a pair of entangled qubits implemented by a fiber-optic polarization dependent loss emulator

The ability to distribute entanglement to remote locations is an essential feature of future quantum networks. The quality of entanglement could suffer during transmission due to interactions with the transmitting channels. One of the impairments inherent specifically to optical fiber routes is polarization dependent loss (PDL). For the first time we provide a comprehensive treatment of PDL as a local filtering operation. By utilizing the rotational form of the filtering operator we are able to obtain analytical expressions for the entanglement metrics of a pair of polarization-entangled qubits traversing channels with PDL of arbitrary magnitude and orientation. We then generalize our approach by considering the effect of PDL on partially entangled states such as Bell diagonal states and Werner states. We further find the conditions for which local filtering in one channel can compensate for the effect of PDL in the other channel. Finally, we use our quantum networking fiber-optic telecom testbed to verify some of our theoretical findings experimentally. We are able to degrade the entanglement by introducing controlled PDL element in one channel and to compensate its effect by a properly matched PDL element in the other channel.