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

[2512.23599] Paradox-free classical non-causality and unambiguous non-locality without entanglement are equivalent Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2512.23599 (quant-ph) [Submitted on 29 Dec 2025 ( v1 ), last revised 27 Aug 2026 (this version, v2)] 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 View PDF HTML (experimental) 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 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 implies, inter alia, that bipartite unambiguous QNLWE bases do not exist. Finally, this work reveals an unexpected connection between causal and non-signaling inequalities: every process function both maximally violates an associated causal inequality and yields a corresponding Bell inequality that admits no violation. Comments: 15+9 pages, 3 figures. Removed the V1 characterization of process functions, which had a loophole (implicit dimension constraints); this will be addressed in future work. Simplified the proof that process functions can be constructed from unambiguous product bases, now relying solely on the unique fixed-point condition. Improved overall manuscript structure Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.23599 [quant-ph] (or arXiv:2512.23599v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.23599 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hippolyte Dourdent [ view email ] [v1] Mon, 29 Dec 2025 16:51:30 UTC (354 KB) [v2] Thu, 27 Aug 2026 19:03:21 UTC (199 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-12 References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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