The Grothendieck Game and Self-Testing Continuous Groups
Abstract
Self-testing certifies quantum states and measurements from observed correlations alone, without requiring a description of the devices that produce them. In this work we establish, to the best of our knowledge, the first robust self-test of the full continuous family of measurements generated by Majorana operators. We achieve this by showing that the Grothendieck game, a two-player nonlocal game in which the players receive directions on a sphere and return binary answers, is a self-test of Majorana observables. That is, any near-optimal performance certifies an entire continuously parameterized family of quantum measurements. We further extend this certification to products of Majorana observables, obtaining a robust self-test of the spin representation of the continuous pin group.
Related
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- Spectral Rigidity in Toroidal Grothendieck Rings and Multiparameter Quantum Groups
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- Separately continuous maps into regular spaces and continuity of operations in separable semitopological groups
BibTeX
@misc{kulpe2026grothendieck,
title = {{The Grothendieck Game and Self-Testing Continuous Groups}},
author = {Alexander Kulpe and Giulio Malavolta and Simon Schmidt and Michael Walter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06755},
eprint = {2610.06755},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06755},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Grothendieck Game and Self-Testing Continuous Groups
AU - Alexander Kulpe
AU - Giulio Malavolta
AU - Simon Schmidt
AU - Michael Walter
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06755
UR - https://arxiv.org/abs/2610.06755
AB - Self-testing certifies quantum states and measurements from observed correlations alone, without requiring a description of the devices that produce them. In this work we establish, to the best of our knowledge, the first robust self-test of the full continuous family of measurements generated by Majorana operators. We achieve this by showing that the Grothendieck game, a two-player nonlocal game in which the players receive directions on a sphere and return binary answers, is a self-test of Majorana observables. That is, any near-optimal performance certifies an entire continuously parameterized family of quantum measurements. We further extend this certification to products of Majorana observables, obtaining a robust self-test of the spin representation of the continuous pin group.
ER -