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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2412.20126 |
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| _version_ | 1866911087654338560 |
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| author | Liu, Yuan Ramanathan, Ravishankar |
| author_facet | Liu, Yuan Ramanathan, Ravishankar |
| contents | 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 $\log_2 d$ bits of randomness from a qu$d$it system with projective measurements for $d \geq 3$. We analytically derive the Lovász 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 $ε\in [0,1)$. 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 \textit{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal and Feasible Contextuality-based Randomness Generation Liu, Yuan Ramanathan, Ravishankar Quantum Physics 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 $\log_2 d$ bits of randomness from a qu$d$it system with projective measurements for $d \geq 3$. We analytically derive the Lovász 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 $ε\in [0,1)$. 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 \textit{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. |
| title | Optimal and Feasible Contextuality-based Randomness Generation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.20126 |