Undecidability and incompleteness in quantum information theory and operator algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914948273143808 |
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| author | Goldbring, Isaac |
| author_facet | Goldbring, Isaac |
| contents | 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 Gödelian 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08342 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Undecidability and incompleteness in quantum information theory and operator algebras Goldbring, Isaac Logic Computational Complexity Operator Algebras Quantum Physics 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 Gödelian 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. |
| title | Undecidability and incompleteness in quantum information theory and operator algebras |
| topic | Logic Computational Complexity Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2409.08342 |