Quantum Randomness Certification Through Three-state Discrimination

Consider a device which, on each round, prepares one pure quantum state out of three possible ones. The overlaps between the possible states are
$\vert \langle\psi_{0}\vert \psi_{1}\rangle\vert \geq\delta, \vert \langle\psi_{0}\vert \psi_{2}\rangle\vert \geq\Delta_{02}$
and
$\vert \langle\psi_{1}\vert \psi_{2}\rangle\vert \geq\Delta_{12}$
. A measurement will be performed on each round. Our goal is to certify the amount of randomness that can be extracted from the measurement.