Achieving Maximal Causal Indefiniteness in a Maximally Nonlocal Theory

• URL: http://arxiv.org/abs/2411.04201v1
• Date: Wed, 06 Nov 2024 19:01:47 GMT
• Title: Achieving Maximal Causal Indefiniteness in a Maximally Nonlocal Theory
• Authors: Kuntal Sengupta,
• Abstract summary: We show that in maximal theories, respecting non-signalling relations, single system state-spaces do not admit superposition; however, composite systems do. We provide a concrete example of a maximally Bell-nonlocal theory, which allows for post-quantum violations of theory-independent inequalities. 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.
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• Abstract: 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.

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