In this work, we present a biexciton state population in (111)B oriented site-controlled InGaAs quantum dots (QDs) by resonant two photon excitation. We show that the excited state recombines emitting highly pure single photon pairs entangled in polarization. The discussed cases herein are compelling due to the specific energetic structure of Pyramidal InGaAs QDs - an antibinding biexciton - a state with a positive binding energy. We demonstrate that resonant two-photon excitation of QDs with antibinding biexcitons can lead to a complex excitation-recombination scenario. We systematically observed that the resonant biexciton state population is competing with an acoustic-phonon assisted population of an exciton state. These findings show that under typical two-photon resonant excitation conditions deterministic biexciton state initialization can be compromised. This complication should be taken into account by the community members aiming to utilise similar epitaxial QDs with an antibinding biexciton.
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