A non-robust quantum correlation self-test

Abstract:We show that exact self-testing of a quantum correlation does not imply robust self-testing. Mančinska and Schmidt previously established such a separation for non-local games, but their obstruction to robustness arises from two distinct optimal correlations, with the self-tested one remaining robust. We establish the separation for a single correlation. Our proof is operator-algebraic. The main technical contribution is a general construction that associates a synchronous binary correlation to any finitely presented C*-algebra with unitary generators and real-coefficient relations. The implementing states of the correlation correspond exactly to the tracial states on the algebra. We apply this construction to an algebra with a unique finite-dimensional tracial state and a distinct amenable tracial state. By a characterization established by Zhao and independently by Kar, the resulting correlation is a self-test but not a robust self-test.

arXiv:2609.25117 [quant-ph]

(or arXiv:2609.25117v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.25117 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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