Undecidability and incompleteness in quantum information theory and operator algebras

Isaac Goldbring

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arXiv · 2409.08342

Undecidability and incompleteness in quantum information theory and operator algebras

Isaac Goldbring

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Abstract

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.

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BibTeX RIS

Isaac Goldbring. 2024-09-12. Undecidability and incompleteness in quantum information theory and operator algebras. https://arxiv.org/abs/2409.08342

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