Emmanuel M. Pothos

Scientific inquiry seeks causal explanations of observed phenomena. The Bell experiment provides a paradigmatic case, revealing correlations between spatially separated systems that no local model can reproduce. Such correlations, known as Bell non-locality, are typically analyzed under the non-signalling assumption, which requires that local statistics be independent of distant measurement choices. Yet real experiments, as well as applications beyond physics, often involve signalling, raising the question of how non-locality should be characterized without this constraint. We introduce a general method for quantifying Bell non-locality in the presence of signalling, designed to relax locality as little as necessary. Our approach is guided by the question: how often can locality be preserved across repeated trials in explaining the observed correlations? The task reduces to finding the optimal convex decomposition of the observed correlations into local and non-local components. We solve this problem within the linear-programming framework, obtaining a closed-form solution valid for arbitrary correlations. We further evaluate a corresponding measure of signalling, demonstrating the generality of the method and the non-trivial character of the results. By extending the analysis of non-locality outside the non-signalling regime, our framework broadens the scope of experimental analysis both within and beyond physics, offering tools for settings where signaling and non-local contributions are difficult to disentangle.

Human achievement, whether in culture, science, or technology, is unparalleled in the known existence. This achievement is tied to the enormous communities of knowledge, made possible by language. We trace how the principle ‘᾿Eν ἀρχῇ ἦν ὁ λόγος’ (in the beginning was the word) was extended beyond its theological origins and heightened the value of written intelligence throughout Western societies. There lies the challenge regarding modern-age chatbots: they can ‘do’ language apparently as well as ourselves, and there is a natural question of whether they can be considered intelligent, in the same way as we are or otherwise. Are humans uniquely intelligent? We consider this question in terms of the psychological literature on intelligence, evidence for intelligence in non-human animals, the role of written language in science and technology, progress with artificial intelligence, the history of intelligence testing (for both humans and machines), and the role of embodiment in intelligence. We think that it is increasingly difficult to consider humans uniquely intelligent. There are current limitations in chatbots, e.g., concerning perceptual and social awareness, but much attention is currently devoted to overcoming such limitations.

Finding the global minimum of a function with many local extrema is well known to be a challenging computational task. We propose a hybrid quantum–classical algorithm for this optimisation problem, based on a combination of Grover quantum search and the classical Newton–Raphson method. The approach is tailored to situations with a large number of false minima. The main idea is to use quantum search to efficiently locate the vicinity of the true optimum, after which a classical algorithm can solve the problem in only a few iterations. We specifically address the nontrivial question of choosing the discretisation of the function domain, which is critical for quantum approaches to optimisation of continuous functions. While we do not expect that this method will always be superior, we identify a paradigmatic case of a function for which we demonstrate that, remarkably, our hybrid method quadratically outperforms a purely classical approach (measuring performance by the number of function/oracle calls). We evaluate key performance metrics of the algorithm in numerical experiments. We furthermore discuss its possible extensions as well as the potential relevance of hybrid approaches in the context of quantum cognition.

Measurement is a key element of quantum theory where only one possible outcome comes to pass, while other ones disappear. Similar phenomena have been observed in psychology, language processing, and economics. Mathematical descriptions that employ elements of quantum theory have successfully modeled effects observable outside of subatomic physics. Price and value are important concepts in finance. We distinguish between price as something fixed in a transaction and publicly available, while value is an agent’s private assessment. Measurement and updates of both may happen in asynchronous timelines and the frequency of measurements might impact change. When considering derivative markets, usually the focus is on price dynamics given by a stochastic process – market liquidity is often assumed to be infinite. A more detailed consideration of liquidity in relation to price dynamics is desirable and this work outlines possible angles from quantum-inspired models. We discuss how market liquidity and volatility relate to each other in the residential real estate and stock market. We investigate quantum walks, quantum models of psychological decision making by individuals and groups, and the role that the framing of a question plays, all with the goal of an improved understanding of the link between observed price volatility and liquidity.

Legal decision-making is expected to meet high standards of consistency and rationality, yet human judgments in this domain are known to be influenced by procedural factors such as evidence order and intermediate evaluations. Recent work has shown that even legal professionals, including judges, are susceptible to such biases when assessing criminal cases. This raises a critical question: do large language models, which are increasingly proposed as decision-support tools in legal contexts, exhibit similar procedural biases—and if so, can these biases be mitigated? To address this question, we tested GPT-4o and GPT-5.2 using a controlled legal judgment task adapted from prior human research. The task involved simplified criminal cases in which we systematically manipulated (i) the order of incriminating and exonerating evidence and (ii) whether an intermediate guilt judgment was required before a final decision. Model responses were directly compared to human judgments from the original study. We additionally examined whether prompt engineering strategies, based on current best-practice recommendations, could reduce observed biases. GPT-4o exhibited robust order effects and a form of evaluation bias, although the latter differed in structure from the human pattern. GPT-5.2 showed similar but attenuated effects. Across both models, prompt engineering had limited and inconsistent impact, failing to reliably eliminate procedural sensitivity. These findings suggest that even advanced large language models remain vulnerable to normatively irrelevant procedural influences. More broadly, they advise caution in treating large language models as inherently rational or bias-resistant decision-support systems in high-stakes professional domains such as law.

Large Language Models (LLMs) such as GPT‑5 are increasingly consulted for advice across a wide range of domains, yet little is known about how their probability judgments compare to those of humans. This study examined GPT‑5’s adherence to classical probability rules, focusing on conjunction fallacies, disjunction fallacies, and violations of binary complementarity. Using a large dataset on human probabilistic judgments, in which participants displayed multiple types of fallacies, we tested GPT‑5 on the same task and with matched participant profiles. GPT‑5 produced only single conjunction or disjunction fallacies and showed near‑perfect compliance with binary complementarity constraints. Its overall response pattern aligned with predictions of early quantum‑probabilistic models rather than more recent variants incorporating noise. These findings suggest that GPT‑5 implements a more coherent and internally consistent form of probabilistic reasoning compared to naïve human participants.

The quantum cognition research program concerns the application of quantum probability theory (the rules for how to assign probabilities to events from qua

Studies of order effects have often been siloed into those focused on question order effects, which examine pairs of purportedly independent items, and information order effects, which ask participants to combine multiple pieces of information. We present data from both types of tasks demonstrating a previously unreported asymmetry, where negative stimuli have a stronger effect on subsequent positive stimuli than vice versa. Data are reanalyzed from three previously published studies of order effects, as well as two novel experiments; we observed consistent results across a variety of tasks and stimuli. These results are discussed in the context of both traditional models like Hogarth and Einhorn’s belief-adjustment model and more recent attempts to use quantum probability theory to model order effects.