  The influence of pump coherence on the entanglement produced in spontaneous
parametric down-conversion (SPDC) is important to understand, both from a
fundamental perspective, and from a practical standpoint for controlled
generation of entangled states. In this context, it is known that in the
absence of postselection, the pump coherence in a given degree of freedom (DOF)
imposes an upper limit on the generated entanglement in the same DOF. However,
the cross-influence of the pump coherence on the generated entanglement in a
different DOF is not well-understood. Here, we experimentally investigate the
effect of a spatiotemporally highly-incoherent (STHI) light-emitting diode
(LED) pump on the polarization entanglement generated in SPDC. Our quantum
state tomography measurements using multimode collection fibers to reduce the
influence of postselection yield a two-qubit state with a concurrence of
0.531+/-0.006 and a purity of 0.647+/-0.005, in excellent agreement with our
theoretically predicted concurrence of 0.552 and purity of 0.652. Therefore,
while the use of an STHI pump causes reduction in the entanglement and purity
of the output polarization two-qubit state, the viability of SPDC with STHI
pumps is nevertheless important for two reasons: (i) STHI sources are
ubiquitous and available at a wider range of wavelengths than lasers, and (ii)
the generated STHI polarization-entangled two-photon states could potentially
be useful in long-distance quantum communication schemes due to their
robustness to scattering.
