Optimal and Feasible Contextuality-based Randomness Generation

作     者：Liu, Yuan Ramanathan, Ravishankar 

作者机构：School of Computing and Data Science The University of Hong Kong Pokfulam Road Hong Kong 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Qubits 

摘      要：Semi-device-independent (SDI) randomness generation protocols based on Kochen-Specker contextuality offer the attractive features of compact devices, high rates, and ease of experimental implementation over fully device-independent (DI) protocols. Here, we investigate this paradigm and derive four results to improve the state-of-art. Firstly, we introduce a family of simple, experimentally feasible orthogonality graphs (measurement compatibility structures) for which the maximum violation of the corresponding non-contextuality inequalities allows to certify the maximum amount of log2 d bits from a qudit system with projective measurements for d ≥ 3. We analytically derive the Lovasz theta and fractional packing number for this graph family, and thereby prove their utility for optimal randomness generation in both randomness expansion and amplification tasks. Secondly, a central additional assumption in contextuality-based protocols over fully DI ones, is that the measurements are repeatable and satisfy an intended compatibility structure. We frame a relaxation of this condition in terms of Ε-orthogonality graphs for a parameter Ε 0, and derive quantum correlations that allow to certify randomness for arbitrary relaxation Ε ∈ [0, 1). Thirdly, it is well known that a single qubit is non-contextual, i.e., the qubit correlations can be explained by a non-contextual hidden variable (NCHV) model. We show however that a single qubit is almost contextual, in that there exist qubit correlations that cannot be explained by Ε-faithful NCHV models for small Ε 0. Finally, we point out possible attacks by quantum and general consistent (non-signalling) adversaries for certain classes of contextuality tests over and above those considered in DI scenarios. Copyright © 2024, The Authors. All rights reserved.