Abstract
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, 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 random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit 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.
Highlights
IntroductionThe intrinsic randomness of quantum theory manifested in the outcomes of quantum measurement is one of the most intriguing features of quantum mechanics [1]
We extend the self-testing proof of [17] to certify, up to the transposition equivalence, all of the Weyl–Heisenberg (W-H) operators acting on three-dimensional Hilbert spaces
We introduced a method for device-independent certification of maximal randomness from pure entangled states in dimension three using non-projective measurements
Summary
The intrinsic randomness of quantum theory manifested in the outcomes of quantum measurement is one of the most intriguing features of quantum mechanics [1]. Even more remarkable is the fact that quantum technologies allow us to generate certifiable randomness with an unprecedented level of security [2]. Protocols designed for randomness certification ensure both the generation of completely random bits and their privacy, which for instance introduces new possibilities in designing protocols for tasks such as quantum cryptography and quantum key distribution [3]. [2]), significant progress has been made both in theoretical and experimental aspects [5–8]. It was shown, for instance, in Ref. Wittek–Acín–Pironio (SATWAP) Bell inequality [10] enables self-testing the maximally entangled state of two-qudits of arbitrary local dimension, which in turn allows certifying log d bits of randomness by using projective measurements. The intuitive reason behind this is the existence of extremal d2 -outcome non-projective measurements in d-dimensional Hilbert spaces, which might give rise to
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