Knot invariants and indefinite causal order
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915534116749312 |
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| author | Fedida, Samuel de la Hamette, Anne-Catherine Kabel, Viktoria Brukner, Časlav |
| author_facet | Fedida, Samuel de la Hamette, Anne-Catherine Kabel, Viktoria Brukner, Časlav |
| contents | We explore indefinite causal order between events in the context of quasiclassical spacetimes in superposition. We introduce several new quantifiers to measure the degree of indefiniteness of the causal order for an arbitrary finite number of events and spacetime configurations in superposition. By constructing diagrammatic and knot-theoretic representations of the causal order between events, we find that the definiteness or maximal indefiniteness of the causal order is topologically invariant. This reveals an intriguing connection between the field of quantum causality and knot theory. Furthermore, we provide an operational encoding of indefinite causal order and discuss how to incorporate a measure of quantum coherence into our classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Knot invariants and indefinite causal order Fedida, Samuel de la Hamette, Anne-Catherine Kabel, Viktoria Brukner, Časlav General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics We explore indefinite causal order between events in the context of quasiclassical spacetimes in superposition. We introduce several new quantifiers to measure the degree of indefiniteness of the causal order for an arbitrary finite number of events and spacetime configurations in superposition. By constructing diagrammatic and knot-theoretic representations of the causal order between events, we find that the definiteness or maximal indefiniteness of the causal order is topologically invariant. This reveals an intriguing connection between the field of quantum causality and knot theory. Furthermore, we provide an operational encoding of indefinite causal order and discuss how to incorporate a measure of quantum coherence into our classification. |
| title | Knot invariants and indefinite causal order |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2409.11448 |