  Unwanted multiphoton emission commonly reduces the degree of entanglement of
photons generated by non-classical light sources and, in turn, hampers their
exploitation in quantum information science and technology. Quantum emitters
have the potential to overcome this hurdle but, so far, the effect of
multiphoton emission on the quality of entanglement has never been addressed in
detail. Here, we tackle this challenge using photon pairs from a
resonantly-driven quantum dot and comparing quantum state tomography and
second-order coherence measurements as a function of the excitation power. We
observe that the relative (absolute) multiphoton emission probability is as low
as $p_m= (5.6 \pm 0.6)10^{-4}$ ($p_2= (1.5 \pm 0.3)10^{-6}$) at the maximum
source brightness, values that lead to a negligible effect on the degree of
entanglement. In stark contrast with probabilistic sources of entangled
photons, we also demonstrate that the multiphoton emission probability and the
degree of entanglement remain practically unchanged against the excitation
power for multiple Rabi cycles, despite we clearly observe oscillations in the
second-order coherence measurements. Our results, explained by a theoretical
model that we develop to estimate the actual multiphoton contribution in the
two-photon density matrix, highlight that quantum dots can be regarded as a
multipair-free source of entangled photons in the solid state.
