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.
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BibTeX
@misc{chen2026nonrobust,
title = {{A non-robust quantum correlation self-test}},
author = {Ranyiliu Chen and Yuming Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.25117},
eprint = {2609.25117},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25117},
}
RIS
TY - UNPB
TI - A non-robust quantum correlation self-test
AU - Ranyiliu Chen
AU - Yuming Zhao
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.25117
UR - https://arxiv.org/abs/2609.25117
AB - 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.
ER -