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This research introduces two new families of bipartite Bell inequalities that achieve optimal global randomness certification for quantum systems with arbitrary output dimensions. By leveraging symmetry arguments and maximally entangled states, the study provides concrete realizations where maximal violations certify a specific number of random bits without relying on computational assumptions. These findings advance the theoretical foundations of device-independent cryptography by establishing rigorous bounds for generating certified randomness in complex quantum networks.
Bell inequalities tailored to optimal global randomness certification
arXiv:2606.21362v3 Announce Type: replace Abstract: We present two novel families of bipartite Bell inequalities designed to achieve optimal global randomness certification for an arbitrary number of outputs $d$. We first use symmetry arguments to argue that their maximal quantum violations certify $2\log d$ random bits. For the first family, we construct a quantum realization using $d\times d$ maximally entangled states which provides a quantum violation that we conjecture to be optimal for any $d$. It is then numerically shown that the obtained quantum violation certifies optimal global randomness, up to numerical precision, for $d=3,4$. For the second family, we provide the optimal quantum violation and its quantum realization for any $d$, again using $d\times d$ maximally entangled states and projective measurements over at least two unbiased bases on one of the parties. We self-test this realization for $d=3$, which implies the optimal certification of two fully random trits.
Abstract:We present two novel families of bipartite Bell inequalities designed to achieve optimal global randomness certification for an arbitrary number of outputs $d$. We first use symmetry arguments to argue that their maximal quantum violations certify $2\log d$ random bits. For the first family, we construct a quantum realization using $d\times d$ maximally entangled states which provides a quantum violation that we conjecture to be optimal for any $d$. It is then numerically shown that the obtained quantum violation certifies optimal global randomness, up to numerical precision, for $d=3,4$. For the second family, we provide the optimal quantum violation and its quantum realization for any $d$, again using $d\times d$ maximally entangled states and projective measurements over at least two unbiased bases on one of the parties. We self-test this realization for $d=3$, which implies the optimal certification of two fully random trits.
See also the related works by R. D'Avino et al and M. Farkas et al. today on arXiv.org
arXiv:2606.21362 [quant-ph]
(or arXiv:2606.21362v3 [quant-ph] for this version)
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