Undecidability and incompleteness in quantum information theory and operator algebras
<|reference_start|>Undecidability and incompleteness in quantum information theory and operator algebras: We survey a number of incompleteness results in operator algebras stemming from the recent undecidability result in quantum complexity theory known as $\operatorname{MIP}^*=\operatorname{RE}$, the most prominent of which is the G\"odelian refutation of the Connes Embedding Problem. We also discuss the very recent use of $\operatorname{MIP}^*=\operatorname{RE}$ in refuting the Aldous-Lyons conjecture in probability theory.<|reference_end|>
@article{goldbring2024undecidability,
    title={Undecidability and incompleteness in quantum information theory and
  operator algebras},
    author={Isaac Goldbring},
    journal={arXiv preprint arXiv:2409.08342},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.08342},
    primaryClass={math.LO cs.CC math.OA quant-ph}
}