  In this report the decoherence sources for entangled photons created by
spontaneous parametric down conversion phenomenon is studied. The phase and
spatial distinguishability of photon pairs from orthogonal crystals reduce the
maximum achievable entanglement fidelity. Carefully chosen compensation
crystals are used to erase the phase and spatial traces of down conversion
origins. Emission angle of photon pairs also leads to optical path difference
and resulting in phase distinguishability. A realistic scenario is numerically
modelled, where the photon pairs with nonzero emission angle gather a phase
difference. These pairs can still be collected and manipulated for practical
use but the collection optics adds upon the phase difference. Two commercially
available optics for collection; aspheric and achromatic lenses are compared.
The numerical simulation results are compared with the experimental results to
validate the built model for predicting the maximum achievable entanglement
fidelity. The results indicate that the fidelity can be accurately estimated
with the presented model by inserting the experimental parameters to it. The
study is expected to be very useful for preparation and optimization of
entangled photon pair sources in critical phase-matching configuration.
