Quantum and non-signalling graph isomorphisms

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Quantum and non-signalling graph isomorphisms

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Quantum and non-signalling graph isomorphisms

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Combinatorial Theory. Series B

ISSN

0095-8956

e-ISSN

—

Svazek periodika

136

Číslo periodika v rámci svazku

May

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

40

Strana od-do

289-328

Kód UT WoS článku

000462695000014

EID výsledku v databázi Scopus

2-s2.0-85057881619