A temporal counterpart to Bell nonlocality would intuitively refer to the presence of non-classical correlations between timelike-separated events. The hypothesis of temporal nonlocality has received recent support in the literature, and its existence would likely influence the future development of physical theories. This paper shows how Adlam's principle of temporal locality can be violated within a protocol involving indefinite causal orders. While the derivations of Leggett-Garg inequalities or the temporal CHSH inequality are said to involve problematic assumptions preventing a targeted probing of a well-defined notion of temporal nonlocality, the present test is free from such worries. However, it is shown that the test, in its current formulation, fails to be fully model-independent. We provide several considerations regarding the physicality of ICOs that could help alleviate this drawback. In the present work, a specific physical interpretation of ICOs in terms of retrocausal influences would explain the presence of temporally nonlocal correlations. It is argued that, as the physical underpinnings of temporal nonlocality might also account for standard Bell nonlocality, focusing on the former as a consequence of ICOs might support under-explored strategies to make sense of the latter.
A temporal counterpart to Bell nonlocality would intuitively refer to the presence of non-classical correlations between timelike-separated events. The hypothesis of temporal nonlocality has received recent support in the literature, and its existence would likely influence the future development of physical theories. This paper shows how Adlam's principle of temporal locality can be violated within a protocol involving indefinite causal orders. While the derivations of Leggett-Garg inequalities or the temporal CHSH inequality are said to involve problematic assumptions preventing a targeted probing of a well-defined notion of temporal nonlocality, the present test is free from such worries. However, it is shown that the test, in its current formulation, fails to be fully model-independent. We provide several considerations regarding the physicality of ICOs that could help alleviate this drawback. In the present work, a specific physical interpretation of ICOs in terms of retrocausal influences would explain the presence of temporally nonlocal correlations. It is argued that, as the physical underpinnings of temporal nonlocality might also account for standard Bell nonlocality, focusing on the former as a consequence of ICOs might support under-explored strategies to make sense of the latter.
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.
In classical physics, events follow a definite causal order: the past influences the future, but not the reverse. Quantum theory, however, permits superpositions of causal orders—the so-called indefinite causal orders (ICOs)—which can provide operational advantages over classical scenarios. Verifying such phenomena has sparked significant interest, much like earlier efforts devoted to refuting local realism and confirming quantum entanglement. To date, demonstrations of ICO have all been based a process called the quantum switch and have relied on device-dependent or semi-device-independent protocols. Achieving a device-independent verification of ICO would imply that nature allows for correlations that do not respect causality, independent of any experimental assumptions or underlying theoretical description of the experiment. To this end, a recent theoretical development introduced a Bell-like inequality that allows for fully device-independent verification of ICO in a quantum switch. Here we implement this verification by experimentally violating this inequality. In particular, we measure a value of 1.8328 ± 0.0045 , which is 18 standard deviations above the definite causal order bound of 1.75 . Our work presents the first implementation of a device-independent protocol to verify ICO, albeit in the presence of experimental loopholes. This represents an important step toward the device-independent verification of an ICO and provides a context in which to identify loopholes specifically related to the verification of ICO.
According to the general theory of relativity, time can flow at different rates depending on the configuration of massive objects, affecting the temporal order of events. Combined with quantum theory, this gravitational effect can result in events with an indefinite temporal order when a massive object is prepared in a suitable quantum state. This was argued to lead to a theory-independent test of the nonclassical order of events through the violation of Bell-type inequalities for temporal order. Here we show that the theory independence of this protocol is problematic: one of the auxiliary assumptions in the above approach turns out to be essential, while it is explicitly theory dependent. To illustrate this problem, we construct a complete scenario where accelerating particles interacting with optical cavities result in a violation of temporal Bell inequalities. Due to the equivalence principle, the same problem arises when one considers the gravitational case, and thus theory-dependent additional assumptions are needed behind Bell inequalities for temporal order to interpret a violation of the final inequalities as a signature of indefinite temporal order.
The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. Here, we present the first demonstration of indefinite temporal order outside of quantum formalism. We show that our experimental outcomes are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality using entangled temporal order. This provides experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.
Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and they are key resources for quantum advantage in information-processing tasks.Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure.Contextuality, on the other hand, is on a more controversial foundation.In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality.First, I show that Bell inequalities can be derived solely from the assumptions of no signaling and no fine-tuning of the causal model.This removes two extra assumptions from a recent result from Wood and Spekkens and, remarkably, does not require any assumption related to independence of measurement settings-unlike all other derivations of Bell inequalities.I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning.Thus, the quantum violation of classical causality goes beyond the case of spacelike-separated systems and already manifests in scenarios involving single systems.
Bell scenarios are multipartite scenarios that exclude any communication between parties. This constraint leads to a strict hierarchy of correlation sets in such scenarios, namely, classical, quantum, and nonsignaling. However, without any constraints on communication between the parties, they can realize arbitrary correlations by exchanging only classical systems. Here we consider a multipartite scenario where the parties can engage in at most a single round of communication, i.e., each party is allowed to receive a system once, implement any local intervention on it, and send out the resulting system once. While no global assumption about causal relations between parties is assumed in this scenario, 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 introduce antinomicity, a notion of nonclassicality for correlations in such scenarios, and prove the existence of a strict hierarchy of correlation sets classified by their antinomicity. Antinomicity serves as a generalization of Bell nonlocality: when all the parties discard their output systems (i.e., in a nonsignaling scenario), it is mathematically equivalent to Bell nonlocality. Like Bell nonlocality, it can be understood as an instance of fine-tuning, one that is necessary in any classical model of cyclic causation that avoids time-travel antinomies but allows antinomic correlations. Furthermore, antinomicity resolves a long-standing puzzle, i.e., the failure of causal inequality violations as device-independent witnesses of nonclassicality. Antinomicity implies causal inequality violations, but not conversely.