Achieving Maximal Causal Indefiniteness in a Maximally Nonlocal Theory
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908122417725440 |
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| author | Sengupta, Kuntal |
| author_facet | Sengupta, Kuntal |
| contents | Quantum theory allows for the superposition of causal orders between operations, i.e., for an indefinite causal order; an implication of the principle of quantum superposition. Since a higher theory might also admit this feature, an understanding of superposition and indefinite causal order in a generalised probabilistic framework is needed. We present a possible notion of superposition for such a framework and show that in maximal theories, respecting non-signalling relations, single system state-spaces do not admit superposition; however, composite systems do. Additionally, we show that superposition does not imply entanglement. Next, we provide a concrete example of a maximally Bell-nonlocal theory, which not only admits the presented notion of superposition, but also allows for post-quantum violations of theory-independent inequalities that certify indefinite causal order; even up to an algebraic bound. These findings might point towards potential connections between a theory's ability to admit indefinite causal order, Bell-nonlocal correlations and the structure of its state spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Achieving Maximal Causal Indefiniteness in a Maximally Nonlocal Theory Sengupta, Kuntal Quantum Physics Quantum theory allows for the superposition of causal orders between operations, i.e., for an indefinite causal order; an implication of the principle of quantum superposition. Since a higher theory might also admit this feature, an understanding of superposition and indefinite causal order in a generalised probabilistic framework is needed. We present a possible notion of superposition for such a framework and show that in maximal theories, respecting non-signalling relations, single system state-spaces do not admit superposition; however, composite systems do. Additionally, we show that superposition does not imply entanglement. Next, we provide a concrete example of a maximally Bell-nonlocal theory, which not only admits the presented notion of superposition, but also allows for post-quantum violations of theory-independent inequalities that certify indefinite causal order; even up to an algebraic bound. These findings might point towards potential connections between a theory's ability to admit indefinite causal order, Bell-nonlocal correlations and the structure of its state spaces. |
| title | Achieving Maximal Causal Indefiniteness in a Maximally Nonlocal Theory |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.04201 |