  Spontaneous parametric down-conversion (SPDC) is a reliable platform for
entanglement generation. Routinely, a coherent laser beam is an essential
prerequisite for pumping the nonlinear crystal. Here we break this barrier to
generate polarization entangled photon pairs by using a commercial
light-emitting diode (LED) source to serve as the pump beam. This effect is
counterintuitive, as the LED source is of extremely low spatial coherence,
which is transferred during the down-conversion process to the biphoton
wavefunction. However, the type-II phase-matching condition naturally filters
the specific frequency and wavelength of LED light exclusively to participate
in SPDC such that localized polarization Bell states can be generated,
regardless of the global incoherence over the full transverse plane. In our
experiment, we characterize the degree of LED light-induced polarization
entanglement in the standard framework of the violation of Bell inequality. We
have achieved the Bell value $S=2.33\pm 0.097$, obviously surpassing the
classical bound $S=2$ and thus witnessing the quantum entanglement. Our work
can be extended to prepare polarization entanglement by using other natural
light sources, such as sunlight and bio-light, which holds promise for
electricity-free quantum communications in outer space.
