Quantum and non-signalling graph isomorphisms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10405099" target="_blank" >RIV/00216208:11320/19:10405099 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=E5HJ0cgVtc" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=E5HJ0cgVtc</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2018.11.002" target="_blank" >10.1016/j.jctb.2018.11.002</a>
Alternative languages
Result language
angličtina
Original language name
Quantum and non-signalling graph isomorphisms
Original language description
We introduce the (G, H) isomorphism game, a new two-player non-local game that classical players can win with certainty iff the graphs G and H are isomorphic. We then define quantum and non-signalling isomorphisms by considering perfect quantum and non-signalling strategies for this game. We prove that non-signalling isomorphism coincides with fractional isomorphism, giving the latter an operational interpretation. We show that quantum isomorphism is equivalent to the feasibility of two polynomial systems obtained by relaxing standard integer programs for graph isomorphism to Hermitian variables. Finally, we provide a reduction from linear binary constraint system games to isomorphism games. This reduction provides examples of quantum isomorphic graphs that are not isomorphic, implies that the tensor product and commuting operator frameworks result in different notions of quantum isomorphism, and proves that both relations are undecidable. (C) 2018 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Combinatorial Theory. Series B
ISSN
0095-8956
e-ISSN
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Volume of the periodical
136
Issue of the periodical within the volume
May
Country of publishing house
US - UNITED STATES
Number of pages
40
Pages from-to
289-328
UT code for WoS article
000462695000014
EID of the result in the Scopus database
2-s2.0-85057881619