Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems

Entanglement in bipartite systems has been applied to generate secure random numbers, which are playing an important role in cryptography or scientific numerical simulations. Here, we propose to use multipartite entanglement distributed between trusted and untrusted parties for generating randomness of arbitrary dimensional systems. We show that the distributed structure of several parties leads to additional protection against possible attacks by an eavesdropper, resulting in more secure randomness generated than in the corresponding bipartite scenario. Especially, randomness can be certified in the group of untrusted parties, even when there is no randomness in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when each untrusted party has a choice between only two measurements. However, the sufficiency no longer holds with more measurement settings. Finally, we apply our analysis to some experimentally realized states and show that more randomness can be extracted compared with the existing analysis.