Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems

Abstract

Entanglement in bipartite systems has been applied for the generation of 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 there is no randomness exists in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when two measurement settings are performed on the untrusted parties. 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 in comparison to the existing analysis.

14 pages, 5 figures

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Cited by in corpus (11)

• Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems
• One-Sided Device-Independent Random Number Generation Through Fiber Channels
• Detecting quantum steering in networks
• Randomness versus Nonlocality in Multi-input and Multi-output Quantum Scenario
• Imprecision plateaus in quantum steering
• Necessary and Sufficient Condition for Randomness Certification from Incompatibility
• Quantifying Quantum Steering with Limited Resources: A Semi-supervised Machine Learning Approach
• Phase-selective tripartite entanglement and asymmetric Einstein-Podolsky-Rosen steering in squeezed optomechanics
• Threshold (Q, P) Quantum Distillation
• Multipartite steering verification with imprecise measurements
• Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum--one-photon superpositions