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While it has recently been demonstrated how to certify the maximal amount ofrandomness from any pure two-qubit entangled state in a device-independent way[E. Woodhead et al., Phys. Rev. Research 2, 042028(R)(2020)], the problem ofoptimal randomness certification from entangled states of higher localdimension remains open. Here we introduce a method for device-independentcertification of the maximal possible amount of $2\log_23$ random bits usingpure bipartite entangled two-qutrit states and extremal nine-outcome generalnon-projective measurements. To this aim, we exploit the extended Bell scenariointroduced recently in [S. Sarkar et al., arXiv:2110.15176], which combines adevice-independent method for certification of the full Weyl-Heisenberg basisin three-dimensional Hilbert spaces together with a one-sideddevice-independent method for certification of two-qutrit partially entangledstates.

Device-independent certification of maximal randomness from pure entangled two-qutrit states using non-projective measurements