Certified upper bounds approach the bulk gap, while a halting-problem reduction rules out a general lower-bounding algorithm, even in one dimension. Convergent upper bounds have no computable rate in general. Full SU(2) symmetry improves our kagome bounds.
An operator-algebraic characterization of the mixed model for tree networks proves convergence of quantum inflation and a new source-transfer hierarchy, extending noncommutative polynomial optimization to multiple states linked by completely positive maps.
Using self-testing, we prove that fermionic correlations in distributed computation cannot be reproduced by any qubit- or boson-based protocol without additional communication, establishing an operational advantage for fermionic information carriers—febits.
A complete semidefinite hierarchy for quantum instruments gives quantitative upper bounds for all multipartite compiled nonlocal games, connecting cryptographic soundness to the structure of sequential quantum strategies.
@misc{dmello2026operationalcharacterizationfinitedimensionalquantum,
title = {An operational characterization of finite-dimensional quantum theory},
author = {Lionel J. Dmello and Xiangling Xu and Marc-Olivier Renou and David Gross},
year = {2026},
eprint = {2610.03694},
archiveprefix = {arXiv},
primaryclass = {quant-ph},
url = {https://arxiv.org/abs/2610.03694},
}
@misc{xu2026quantumtreenetworkscomplete,
title = {Quantum inflation and source-transfer hierarchies are complete for tree networks},
author = {Xiangling Xu and Igor Klep and Marc-Olivier Renou},
year = {2026},
date = {2026-09-16},
eprint = {2609.19310},
archiveprefix = {arXiv},
primaryclass = {quant-ph},
url = {https://arxiv.org/abs/2609.19310},
}
@misc{kalarde2026fermionsfundamentallynonlocalbosons,
title = {Fermions are fundamentally more nonlocal than Bosons},
author = {Moradi Kalarde, Fatemeh and Boreiri, Sadra and Xu, Xiangling and Tendick, Lucas and Beigi, Salman and Perinotti, Paolo and Guaita, Tommaso and Renou, Marc-Olivier},
year = {2026},
date = {2026-06},
eprint = {2606.12363},
archiveprefix = {arXiv},
primaryclass = {quant-ph},
url = {https://arxiv.org/abs/2606.12363},
}
@misc{xu2026bulkspectralgapcertifiable,
title = {The bulk spectral gap is certifiable from above but uncomputable from below},
author = {Xu, Xiangling and Sch{\"o}tz, Matthias and Wang, Jie and Magron, Victor and Klep, Igor and Fawzi, Omar and Renou, Marc-Olivier},
year = {2026},
eprint = {2606.03836},
archiveprefix = {arXiv},
primaryclass = {quant-ph},
url = {https://arxiv.org/abs/2606.03836},
}
@misc{kalarde2026commentquantumtheorybased,
title = {Comment on "{Quantum theory based on real numbers cannot be experimentally falsified}": On the compatibility of physical principles with information theory for fermions},
author = {Fatemeh Moradi Kalarde and Xiangling Xu and Marc-Olivier Renou},
year = {2026},
date = {2026-04},
eprint = {2604.07425},
archiveprefix = {arXiv},
primaryclass = {quant-ph},
url = {https://arxiv.org/abs/2604.07425},
}
@article{renou2024convergentnpalikehierarchiesquantum,
title = {Two convergent {NPA}-like hierarchies for the quantum bilocal scenario},
author = {Renou, Marc-Olivier and Xu, Xiangling and Ligthart, Laurens T.},
journal = {Journal of Mathematical Physics},
volume = {67},
number = {1},
eid = {012203},
year = {2026},
month = {01},
doi = {10.1063/5.0211008},
url = {https://doi.org/10.1063/5.0211008},
issn = {0022-2488},
}
@misc{baroni2025quantitativequantumsoundnessmultipartite,
title = {Quantitative quantum soundness for all multipartite compiled nonlocal games},
author = {Baroni, Matilde and Klep, Igor and Leichtle, Dominik and Renou, Marc-Olivier and {\v{S}}upi{\'c}, Ivan and Tendick, Lucas and Xu, Xiangling},
year = {2025},
date = {2025-09},
eprint = {2509.25145},
archiveprefix = {arXiv},
primaryclass = {quant-ph},
url = {https://arxiv.org/abs/2509.25145},
}
@misc{xu2025quantitativetsirelsonstheoremsapproximate,
title = {Quantitative {Tsirelson}'s Theorems via Approximate {Schur}'s Lemma and Probabilistic {Stampfli}'s Theorems},
author = {Xu, Xiangling and Renou, Marc-Olivier and Klep, Igor},
year = {2025},
date = {2025-05},
eprint = {2505.22309},
archiveprefix = {arXiv},
primaryclass = {quant-ph},
url = {https://arxiv.org/abs/2505.22309},
}
@misc{klep2025quantitativequantumsoundnessbipartite,
title = {Quantitative Quantum Soundness for Bipartite Compiled {Bell} Games via the Sequential {NPA} Hierarchy},
author = {Klep, Igor and Paddock, Connor and Renou, Marc-Olivier and Schmidt, Simon and Tendick, Lucas and Xu, Xiangling and Zhao, Yuming},
year = {2025},
date = {2025-07},
eprint = {2507.17006},
archiveprefix = {arXiv},
primaryclass = {quant-ph},
url = {https://arxiv.org/abs/2507.17006},
}
@article{luo2023kinematic,
title = {On the kinematic morphology around haloes},
author = {Luo, Xiaolin and Xu, Xiangling and Wang, Xin},
journal = {Monthly Notices of the Royal Astronomical Society},
volume = {518},
number = {4},
pages = {6059--6064},
year = {2023},
doi = {10.1093/mnras/stac3500},
publisher = {Oxford University Press},
}
@mastersthesis{xu2023quantum,
title = {Quantum Nonlocality in Bilocal Networks: An Operator Algebraic Perspective},
author = {Xu, Xiangling},
school = {ETH Z{\"u}rich},
year = {2023},
doi = {10.3929/ethz-b-000613670},
publisher = {ETH Library Research Collection},
}