The development of scalable sources of non-classical light is fundamental to unlock the technological potential of quantum photonicscite{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 Bells 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.
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