Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2012.13878 · The European Physical Journal D

Semi-device-independent randomness certification using Mermin’s proof of Kochen–Specker contextuality

A. K. Pan

Published Mar 1, 2021• 5 citations
arXivHTMLPDF
DOI
10.1140/epjd/s10053-021-00105-8

Related papers

Optimal measurement structures for contextuality applications

Yuan Liu, Ravishankar Ramanathan, Karol Horodecki +2 more

Abstract The Kochen-Specker (KS) theorem is a corner-stone result in the foundations of quantum mechanics describing the fundamental difference between quantum theory and classical non-contextual theories. Recently specific substructures termed $01$-gadgets were shown to exist within KS proofs that capture the essential contradiction of the theorem. Here, we show these gadgets and their generalizations provide an optimal toolbox for contextuality applications including (i) constructing classical channels exhibiting entanglement-assisted advantage in zero-error communication, (ii) identifying large separations between quantum theory and binary generalised probabilistic theories, and (iii) finding optimal tests for contextuality-based semi-device-independent randomness generation. Furthermore, we introduce and study a generalisation to definite prediction sets for more general logical propositions, that we term higher-order gadgets. We pinpoint the role these higher-order gadgets play in KS proofs by identifying these as induced subgraphs within KS graphs and showing how to construct proofs of state-independent contextuality using higher-order gadgets as building blocks. The constructions developed here may help in solving some of the remaining open problems regarding minimal proofs of the Kochen-Specker theorem.

arXiv:2206.13139•npj Quantum Information•Jun 29, 2023•3 citations

Certified Quantum Randomness: Device-Independent and Semi-Device-Independent Approaches, Experimental Realizations, and Applications

Shyam Sundar Mahato

International Journal of Theoretical Physics•Feb 23, 2026•0 citations

Device-independent randomness certification using multiple copies of entangled states

Shyam Sundar Mahato, A. K. Pan

arXiv:2212.14341•Physics Letters A•Nov 4, 2022•8 citations

SAT + NAUTY: Orderly Generation of Small Kochen-Specker Sets Containing the Smallest State-independent Contextuality Set

Zhengyu Li, Curtis Bright, Stefan Trandafir +2 more

We present a search for small Kochen-Specker (KS) sets in dimension 3, specifically targeting extensions of the 13-ray Yu-Oh set, which has been proven to be the minimal witness to state-independent contextuality. To enable this search, we introduce a novel SAT-based orderly generation framework integrating recursive canonical labeling (RCL) with the graph isomorphism tool NAUTY. We demonstrate that previous SAT approaches relying on lexicographical canonicity suffer from exponential scaling on canonical graphs. This limitation renders them intractable on the large instances (25 to 33 vertices) encountered in our search, whereas our RCL check maintains consistent millisecond-level performance, effectively eliminating the bottleneck. Overcoming this bottleneck allows us to perform the first exhaustive enumeration of all KS sets with up to 33 rays containing the complete 25-ray state-independent contextuality (SI-C) set obtained by rigid extensions of the Yu-Oh set in 1,641 CPU hours. We found and verified that the 33-ray set discovered by Schütte is the smallest three-dimensional KS set containing the complete 25-ray SI-C set. All non-existence results are backed by independently verifiable proof certificates via an extension of the DRAT proof format.

cs.LOCross-listedarXiv:2604.19947•Apr 23, 2026•0 citations

Realization of a Quantum Random Generator Certified with the Kochen-Specker Theorem

Anatoly Kulikov, Markus Jerger, Anton Potočnik +2 more

Random numbers are required for a variety of applications from secure communications to Monte Carlo simulation. Yet randomness is an asymptotic property, and no output string generated by a physical device can be strictly proven to be random. We report an experimental realization of a quantum random number generator (QRNG) with randomness certified by quantum contextuality and the Kochen-Specker theorem. The certification is not performed in a device-independent way but through a rigorous theoretical proof of each outcome being value indefinite even in the presence of experimental imperfections. The analysis of the generated data confirms the incomputable nature of our QRNG.

arXiv:1709.03687•Physical Review Letters•Dec 11, 2017•36 citations

Temporal correlations and device-independent randomness

Shiladitya Mal, Manik Banik, Sujit K. Choudhary

Quantum Information Processing•Apr 26, 2016•10 citations
Abstract The Kochen-Specker (KS) theorem is a corner-stone result in the foundations of quantum mechanics describing the fundamental difference between quantum theory and classical non-contextual theories. Recently specific substructures termed 010101-gadgets were shown to exist within KS proofs that capture the essential contradiction of the theorem. Here, we show these gadgets and their generalizations provide an optimal toolbox for contextuality applications including (i) constructing classical channels exhibiting entanglement-assisted advantage in zero-error communication, (ii) identifying large separations between quantum theory and binary generalised probabilistic theories, and (iii) finding optimal tests for contextuality-based semi-device-independent randomness generation. Furthermore, we introduce and study a generalisation to definite prediction sets for more general logical propositions, that we term higher-order gadgets. We pinpoint the role these higher-order gadgets play in KS proofs by identifying these as induced subgraphs within KS graphs and showing how to construct proofs of state-independent contextuality using higher-order gadgets as building blocks. The constructions developed here may help in solving some of the remaining open problems regarding minimal proofs of the Kochen-Specker theorem.
We present a search for small Kochen-Specker (KS) sets in dimension 3, specifically targeting extensions of the 13-ray Yu-Oh set, which has been proven to be the minimal witness to state-independent contextuality. To enable this search, we introduce a novel SAT-based orderly generation framework integrating recursive canonical labeling (RCL) with the graph isomorphism tool NAUTY. We demonstrate that previous SAT approaches relying on lexicographical canonicity suffer from exponential scaling on canonical graphs. This limitation renders them intractable on the large instances (25 to 33 vertices) encountered in our search, whereas our RCL check maintains consistent millisecond-level performance, effectively eliminating the bottleneck. Overcoming this bottleneck allows us to perform the first exhaustive enumeration of all KS sets with up to 33 rays containing the complete 25-ray state-independent contextuality (SI-C) set obtained by rigid extensions of the Yu-Oh set in 1,641 CPU hours. We found and verified that the 33-ray set discovered by Schütte is the smallest three-dimensional KS set containing the complete 25-ray SI-C set. All non-existence results are backed by independently verifiable proof certificates via an extension of the DRAT proof format.
Random numbers are required for a variety of applications from secure communications to Monte Carlo simulation. Yet randomness is an asymptotic property, and no output string generated by a physical device can be strictly proven to be random. We report an experimental realization of a quantum random number generator (QRNG) with randomness certified by quantum contextuality and the Kochen-Specker theorem. The certification is not performed in a device-independent way but through a rigorous theoretical proof of each outcome being value indefinite even in the presence of experimental imperfections. The analysis of the generated data confirms the incomputable nature of our QRNG.