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

While it has recently been demonstrated how to certify the maximal amount of randomness 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 of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of $2\log_23$ random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit the extended Bell scenario introduced recently in [S. Sarkar et al., arXiv:2110.15176], which combines a device-independent method for certification of the full Weyl-Heisenberg basis in three-dimensional Hilbert spaces together with a one-sided device-independent method for certification of two-qutrit partially entangled states.

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