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
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.
Quantum theory admits ensembles of quantum nonlocality without entanglement (QNLWE). These ensembles consist of seemingly classical states (they are perfectly distinguishable and nonentangled) that cannot be perfectly discriminated with local operations and classical communication (LOCC). Here, we analyze QNLWE from a causal perspective, and show how to perfectly discriminate some of these ensembles using local operations and classical communication without definite causal order. Specifically, three parties with access to an instance of indefinite causal order-the Araújo-Feix-Baumeler-Wolf process-can perfectly discriminate the states in a QNLWE ensemble-the SHIFT ensemble-with local operations. Hence, this type of quantum nonlocality disappears at the expense of definite causal order while retaining classical communication. Our results thereby leverage the fact that LOCC is a conjunction of three constraints: local operations, classical communication, and definite causal order. Moreover, we show how multipartite generalizations of the Araújo-Feix-Baumeler-Wolf process are transformed into multiqubit ensembles that exhibit QNLWE. Such ensembles are of independent interest for cryptographic protocols and for the study of separable quantum operations unachievable with LOCC.
Bell and contextuality scenarios are unified within the Acín-Fritz-Leverrier-Sainz hypergraph formalism, in which measurements are hyperedges. Multipartite measurements are obtained from product rules that combine independent contextuality scenarios into a single hypergraph. Several such rules exist: they are structurally distinct, yet yield the same classical, quantum, and boxworld correlations. Here, we show that this difference is not incidental, unveiling an unexpected connection. The measurements of composite Bell scenarios are exactly the process functions, the deterministic classical communication protocols that may be non-causal, i.e., lack a definite causal order without generating paradoxes. Validity of a hyperedge and logical consistency of a process function are thus one and the same condition. This allows us to characterize process functions by normalization and no-signaling alone, providing transformations that generate non-causal process functions from no-communication ones. The product rules, in turn, order process functions by causal structure, from no-communication to non-causality, which yields a graphical criterion for the latter: a process function is non-causal precisely when its hyperedge is generated by the disjunctive but not the maximal product. We thereby obtain the first joint hypergraph representation of (non-causal) process functions and (nonlocal-without-entanglement) measurements, recasting classical non-causality as a non-standard way of composing black boxes.
Bell scenarios are multipartite scenarios that exclude any signalling between parties. This leads to a strict hierarchy of classical, quantum, and non-signalling correlations in such scenarios. Here we consider a minimal relaxation of non-signalling: each party is allowed to receive a system once, implement any local intervention on it, and send out the resulting system once. Crucially, unlike Bell, we make no global assumption about causal relations between parties, e.g., they could be embedded in some exotic spacetime with indefinite causal order. We do make a causal assumption local to each party, i.e., the input received by it causally precedes the output it sends out. We then ask: Can we device-independently certify the nonclassicality of multipartite correlations in such scenarios, just as Bell inequality violations do so in Bell scenarios? A priori, this is not clear: without some assumptions on the underlying physics (e.g., non-signalling), parties can realize arbitrary correlations. We therefore make a minimal assumption of logical consistency on the underlying physics, i.e., it must be free of time-travel antinomies without imposing any restrictions on local interventions of the parties. We then define antinomicity as a device-independent notion of nonclassicality and prove a strict hierarchy between correlation sets based on their antinomicity. An antinomic correlation cannot be explained by a classical physical theory compatible with free local interventions on pain of logical contradictions in the theory. On the other hand, parties exchanging quantum systems can witness antinomicity while respecting logical consistency. Antinomicity reduces to Bell nonlocality for non-signalling parties. It also resolves a conceptual puzzle, namely, the failure of causal inequalities as witnesses of nonclassicality: antinomicity implies causal inequality violations, but not conversely.
We study the nature of entanglement in presence of closed timelike curves (CTCs) and we observe that qubits traveling along a CTC allow unambiguous discrimination of Bell states with Local Operations and Classical Communications (LOCC), and can be further generalized to allow unambiguous discrimination of any finite set of bipartite entangled states using just LOCC, that is otherwise known to be impossible. This enables one to create entanglement using just LOCC. Furthermore, we point out how the existence of CTCs would imply entanglement can be polygamous, and thus contradicting the prior known notions of monogamy of entanglement.
Logical consistency with free local operations is compatible with nontrivial classical communications, where all parties can be both in each other’s past and future—a phenomenon known as noncausality. Noncausal processes, such as the “Lugano process,” violate causal inequalities, yet their physical realizability remains an open question. In contrast, the quantum switch—a physically realizable process with indefinite causal order—can only generate causal correlations. Building on a recently established correspondence [Kunjwal and Baumeler, ] between the SHIFT measurement, which exhibits nonlocality without entanglement, and the Lugano process, we demonstrate that the SHIFT measurement can be implemented using a quantum switch of classical communications in a scenario with quantum inputs. This shows that the structure of the Lugano process can be simulated by a quantum switch and that successful SHIFT discrimination witnesses causal nonseparability rather than noncausality. Finally, we identify a broad class of “superposition of classical communications” derived from classical processes without global past capable of realizing similar causally indefinite measurements. We examine these results in relation to the ongoing debate on implementations of indefinite causal orders.
The no-signalling principle lies at the heart of Bell-type experiments involving spacelike-separated parties. Although not all no-signalling correlations can be realized within quantum theory, the no-sinalling principle itself remains fundamental even for post-quantum theories, since its violation would imply superluminal signalling. In the spirit of device independent nature of the Bell inequalities, there has recently been growing interest in causal inequalities, which identify correlations admitting no causal explanation. Such correlations have been rigorously studied within the process-matrix formalism, which is built upon a constraint analogous to spacelike separation in Bell scenarios. We refer to this constraint as the single-interaction constraint, whereby each party interacts with the environment only once. Despite considerable effort, no fundamental guiding principle is currently known that characterizes the restrictions this constraint imposes on the correlations generated by Process Matrices. In this work, we address this gap by proposing a generalized causality principle for the bipartite case. We show that for certain cases, the generalised causality principle defines a strict subset of the set of all signalling correlations. This principle thus provides a fundamental limit on quantum and even post-quantum theories subject to the single-interaction constraint. By analogy with no-signalling, whose violation excludes certain causal structures among the parties, a violation of the generalised causality principle rules out a corresponding class of causal structures(causal structures with the single interaction constraint). More broadly, our techniques provide a general framework for deriving generalised causal constraints, applicable to a wide class of indefinite-causal-order scenarios.