Quantum no-signalling bicorrelations
Artikel i vetenskaplig tidskrift, 2024

We introduce classical and quantum no-signalling bicorrelations and characterise the different types thereof in terms of states on operator system tensor products, exhibiting connections with bistochastic operator matrices and with dilations of quantum magic squares. We define concurrent bicorrelations as a quantum input-output generalisation of bisynchronous correlations. We show that concurrent bicorrelations of quantum commuting type correspond to tracial states on the universal C*-algebra of the projective free unitary quantum group, showing that in the quantum input-output setup, quantum permutations of finite sets must be replaced by quantum automorphisms of matrix algebras. We apply our results to study the quantum graph isomorphism game, describing the game C*-algebra in this case, and make precise connections with the algebraic notions of quantum graph isomorphism, existing presently in the literature.

Operator system

Non-local games

Entanglement

Quantum graphs

Författare

Michael Brannan

University of Waterloo

Samuel J. Harris

Northern Arizona University

I. G. Todorov

University of Delaware

Lyudmyla Turowska

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Advances in Mathematics

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 449 109732

Ämneskategorier

Matematik

Fysik

DOI

10.1016/j.aim.2024.109732

Mer information

Senast uppdaterat

2024-06-11