  The generation of entanglement between distant atoms via single photons is
the basis for networked quantum computing, a promising route to large-scale
trapped-ion and trapped-atom processors. Locating the emitter within an optical
cavity provides an efficient matter-light interface, but mirror-induced
birefringence within the cavity introduces time-dependence to the polarisation
of the photons produced. We show that such `polarisation oscillation' effects
can lead to severe loss of fidelity in the context of two-photon, polarisation
encoded measurement-based remote entanglement schemes. It is always preferable
to suppress these errors at source by minimising mirror ellipticity, but we
propose two remedies for systems where this cannot be achieved. We conclude
that even modest cavity birefringence can be detrimental to remote entanglement
performance, to an extent that may limit the suitability of
polarisation-encoded schemes for large-scale quantum networks.
