Paradox-free classical non-causality and unambiguous non-locality without entanglement are equivalent

• URL: http://arxiv.org/abs/2512.23599v1
• Date: Mon, 29 Dec 2025 16:51:30 GMT
• Title: Paradox-free classical non-causality and unambiguous non-locality without entanglement are equivalent
• Authors: Hippolyte Dourdent, Kyrylo Simonov, Andreas Leitherer, Emanuel-Cristian Boghiu, Ravi Kunjwal, Saronath Halder, Remigiusz Augusiak, Antonio Acín,
• Abstract summary: We show that non-causality of process functions is exactly mirrored by quantum nonlocality without entanglement (QNLWE)<n>Our results generalize previous special cases to arbitrary local dimensions and any number of parties.
• Score: 0.17425880920540052
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Closed timelike curves (CTCs) challenge our conception of causality by allowing information to loop back into its own past. Any consistent description of such scenarios must avoid time-travel paradoxes while respecting the no-new-physics principle, which requires that the set of operations available within any local spacetime region remain unchanged, irrespective of whether CTCs exist elsewhere. Within an information-theoretic framework, this leads to process functions: deterministic classical communication structures that remain logically consistent under arbitrary local operations, yet can exhibit correlations incompatible with any definite causal order - a phenomenon known as non-causality. In this work, we provide the first complete recursive characterization of process functions and of (non-)causal process functions. We use it to establish a correspondence between process functions and unambiguous complete product bases, i.e., product bases in which every local state belongs to a unique local basis. This equivalence implies that non-causality of process functions is exactly mirrored by quantum nonlocality without entanglement (QNLWE) - the impossibility of perfectly distinguishing separable states using local operations and causal classical communication - for such bases. Our results generalize previous special cases to arbitrary local dimensions and any number of parties, enable systematic constructions of non-causal process functions and unambiguous QNLWE bases, and reveal an unexpected connection between certain non-signaling inequalities and causal inequalities.

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