2 Search Results for "Lal, Raymond"

Document
DOI: 10.4230/LIPIcs.FSCD.2024.28
Commutation Groups and State-Independent Contextuality

Authors: Samson Abramsky, Şerban-Ion Cercelescu, and Carmen-Maria Constantin

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage. We introduce commutation groups presented by generators and relations, and analyse them in terms of a string rewriting system. There is also a linear algebraic construction, a directed version of the Heisenberg group. We introduce contextual words as a general form of contextuality witness. We characterise when contextual words can arise in commutation groups, and explicitly construct non-contextual value assignments in other cases. We give unitary representations of commutation groups as subgroups of generalized Pauli n-groups.
Cite as

Samson Abramsky, Şerban-Ion Cercelescu, and Carmen-Maria Constantin. Commutation Groups and State-Independent Contextuality. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abramsky_et_al:LIPIcs.FSCD.2024.28,
  author =	{Abramsky, Samson and Cercelescu, \c{S}erban-Ion and Constantin, Carmen-Maria},
  title =	{{Commutation Groups and State-Independent Contextuality}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.28},
  URN =		{urn:nbn:de:0030-drops-203572},
  doi =		{10.4230/LIPIcs.FSCD.2024.28},
  annote =	{Keywords: Contextuality, state-independence, quantum mechanics, Pauli group, group presentations, unitary representations}
}
Document
DOI: 10.4230/LIPIcs.CSL.2015.211
Contextuality, Cohomology and Paradox

Authors: Samson Abramsky, Rui Soares Barbosa, Kohei Kishida, Raymond Lal, and Shane Mansfield

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in quantum theory [New Journal of Physics 13 (2011) 113036]. However, contextual phenomena are found in other fields as well, for example database theory. In this paper, we shall develop this unified view of contextuality. We provide two main contributions: firstly, we expose a remarkable connection between contexuality and logical paradoxes; secondly, we show that an important class of contextuality arguments has a topological origin. More specifically, we show that "All-vs-Nothing" proofs of contextuality are witnessed by cohomological obstructions.
Cite as

Samson Abramsky, Rui Soares Barbosa, Kohei Kishida, Raymond Lal, and Shane Mansfield. Contextuality, Cohomology and Paradox. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 211-228, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{abramsky_et_al:LIPIcs.CSL.2015.211,
  author =	{Abramsky, Samson and Soares Barbosa, Rui and Kishida, Kohei and Lal, Raymond and Mansfield, Shane},
  title =	{{Contextuality, Cohomology and Paradox}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{211--228},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.211},
  URN =		{urn:nbn:de:0030-drops-54166},
  doi =		{10.4230/LIPIcs.CSL.2015.211},
  annote =	{Keywords: Quantum mechanics, contextuality, sheaf theory, cohomology, logical paradoxes}
}
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