Undecidability and incompleteness in quantum information theory and operator algebras

• URL: http://arxiv.org/abs/2409.08342v1
• Date: Thu, 12 Sep 2024 18:12:40 GMT
• Title: Undecidability and incompleteness in quantum information theory and operator algebras
• Authors: Isaac Goldbring,
• Abstract summary: We survey a number of incompleteness results in operator algebras stemming from the recent undecidability result in quantum complexity theory. We also discuss the very recent use of $operatornameMIP*=operatornameRE$ in refuting the Aldous-Lyons conjecture in probability theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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