Atserias, A;
Mančinska, L;
Roberson, DE;
Šámal, R;
Severini, S;
Varvitsiotis, A;
(2019)
Quantum and non-signalling graph isomorphisms.
Journal of Combinatorial Theory, Series B
, 136
pp. 289-328.
10.1016/j.jctb.2018.11.002.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | Quantum and non-signalling graph isomorphisms |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jctb.2018.11.002 |
| Publisher version: | https://doi.org/10.1016/j.jctb.2018.11.002 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Graph isomorphism, Quantum strategies, Non-local games, Entanglement, Non-signalling, Fractional isomorphism |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1531352 |
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