  The development of scalable sources of non-classical light is fundamental to
unlock the technological potential of quantum photonics\cite{Kimble:Nat2008}.
Among the systems under investigation, semiconductor quantum dots are currently
emerging as near-optimal sources of indistinguishable single photons. However,
their performances as sources of entangled-photon pairs are in comparison still
modest. Experiments on conventional Stranski-Krastanow InGaAs quantum dots have
reported non-optimal levels of entanglement and indistinguishability of the
emitted photons. For applications such as entanglement teleportation and
quantum repeaters, both criteria have to be met simultaneously. In this work,
we show that this is possible focusing on a system that has received limited
attention so far: GaAs quantum dots grown via droplet etching. Using a
two-photon resonant excitation scheme, we demonstrate that these quantum dots
can emit triggered polarization-entangled photons with high purity
(g^(2)(0)=0.002 +/-0.002), high indistinguishability (0.93 +/-0.07) and high
entanglement fidelity (0.94 +/-0.01). Such unprecedented degree of
entanglement, which in contrast to InGaAs can theoretically reach near-unity
values, allows Bell's inequality (2.64 +/-0.01) to be violated without the aid
of temporal or spectral filtering. Our results show that if quantum-dot
entanglement resources are to be used for future quantum technologies, GaAs
might be the system of choice.
