  Polarization dependent loss (PDL) is a serious problem that hinders the
transfer of polarization qubits through quantum networks. Recently it has been
shown that the detrimental effects of PDL on qubit fidelity can be compensated
for with the introduction of an additional passive PDL element that rebalances
the polarization modes of the transmitted qubit. This procedure works extremely
well when the output of the system is postselected on photon detection.
However, in cases where the qubit might be needed for further analysis this
procedure introduces unwanted vacuum terms into the state. Here we present
procedures for the compensation of the effects of PDL using noiseless
amplification and attenuation. Each of these techniques introduces a heralding
signal into the correction procedure that significantly reduces the vacuum
terms in the final state. When detector inefficiency and dark counts are
included in the analysis noiseless amplification remains superior, in terms of
the fidelity of the final state, to both noiseless attenuation and passive PDL
compensation for detector efficiencies greater than 40%.
