arXiv subjects

Emmanuel M. Pothos

Publications and source records attributed to Emmanuel M. Pothos.

8 recordsLinked to original sources

arXiv2026

The adaptive nature of confirmation bias

In this paper, the phenomenon generally classified as confirmation bias is formulated on the space of square-root probabilities (or equivalently, using the structures of quantum probability). In this framework, observations are modelled by matrices, rather than random variables on a probability space. In the problem of binary hypothesis testing, an optimal evidence choice minimises the expected error probability. We show that the resulting optimal choice of evidence leads to a confirmation bias, thus revealing a surprising aspect of rationality that encompasses confirmation bias. Specifically, in sequential evidence sampling, the implicit optimality leads to two remarkable evolutionary advantages, namely, (a) the decision maker requires only the smallest memory capacity, and (b) the error probability can be reduced exponentially in sample size. A complementary approach based on the framework of active inference -- where the decision maker seeks evidence that provides maximum information -- is then considered. The resulting optimal evidence is shown to agree with the one obtained by minimising error probability. Our framework provides an easy-to-implement protocol for an active quantum inference, whereby the optimal evidence choice for making an inference is sought over the space of matrices.

q-bio.NC↗

arXiv2026

Measuring Bell non-locality in the presence of signaling

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-signaling assumption, which requires that local statistics be independent of distant measurement choices. Yet real experiments, as well as applications beyond physics, often involve signaling, 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 signaling, 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 genuinely 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 signaling, demonstrating the generality of the method and the non-trivial character of the results. By extending the notion of non-locality beyond the non-signaling regime, our framework reshapes the basis for experimental analysis in physics and offers tools applicable outside physics.

quant-ph↗

arXiv2025

High schoolers excel at Oxford quantum course using pictorial mathematics

We are at the dawn of the second quantum revolution, where our ability to create and control individual quantum systems is poised to drive transformative advancements in basic science, computation, and everyday life. However, quantum theory has long been conceived as notoriously hard to learn, creating a significant barrier to workforce development, informed decision-making by stakeholders and policymakers, and broader public understanding. This paper is concerned with Quantum Picturalism, a novel visual mathematical language for quantum physics. Originally developed over two decades ago to explore the foundational structure of quantum theory, this rigorous diagrammatic framework has since been adopted in both academia and industry as a powerful tool for quantum computing research and software development. Here, we demonstrate its potential as a transformative educational methodology. We report the findings from a pilot study involving 54 UK high school students, randomly selected from a pool of 734 volunteers across the UK. Despite the absence of advanced mathematical prerequisites, these students demonstrated a strong conceptual grasp of key quantum principles and operations. On an assessment comprising university graduate-level exam questions, participants achieved an 82% pass rate, with 48% obtaining a distinction-level grade. These results pave the way for making quantum more inclusive, lowering traditional cognitive and demographic barriers to quantum learning. This approach has the potential to broaden participation in the field and provide a promising new entry point for stakeholders, future experts, and the general public.

physics.ed-ph↗

arXiv2025

Natural, Artificial, and Human Intelligences

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: leaving theological content aside, it is very much true that "in the beginning was the word", and that in Western societies, this became particularly identified with the written word. 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.

cs.AI↗

arXiv2025

Incorporating episodic memory into quantum models of judgment and decision

An important challenge for quantum theories of cognition and decision concerns the incorporation of memory for recently made judgments and their effects on later judgments. First, we review a general approach to measurement based on system plus environment representations of states and measurement instruments. These more general measurement models provide ways to incorporate effects of recent judgments on later judgments. Then we compare three different measurement models that are based on these more general measurement operations to a puzzling collection of question order effect findings.

physics.soc-ph↗

arXiv2025

Making the quantum world accessible to young learners through Quantum Picturalism: An experimental study

The educational value of a fully diagrammatic approach in a scientific field has never been explored. We present Quantum Picturalism (QPic), an entirely diagrammatic formalism for all of qubit quantum mechanics. This framework is particularly advantageous for young learners as a novel way to teach key concepts such as entanglement, measurement, and mixed-state quantum mechanics in a math-intensive subject. This eliminates traditional obstacles without compromising mathematical correctness - removing the need for matrices, vectors, tensors, complex numbers, and trigonometry as prerequisites to learning. Its significance lies in that a field as complex as Quantum Information Science and Technology (QIST), for which educational opportunities are typically exclusive to the university level and higher, can be introduced at high school level. In this study, we tested this hypothesis, examining whether QPic reduces cognitive load by lowering complex mathematical barriers while enhancing mental computation and conceptual understanding. The data was collected from an experiment conducted in 2023, whereby 54 high school students (aged 16-18) underwent 16 hours of training spread over eight weeks. The post-assessments illustrated promising outcomes in all three specific areas of focus: (1) whether QPic can alleviate technical barriers in learning QIST, (2) ensures that the content and teaching method are age appropriate, (3) increases confidence and motivation in science and STEM fields. There was a notable success rate in terms of teaching outcomes, with 82% of participants successfully passing an end-of-training exam and 48% achieving a distinction, indicating a high level of performance. The unique testing and training regime effectively reduced the technical barriers typically associated with traditional approaches, as hypothesized.

physics.ed-ph↗

arXiv2021

Violations of locality and free choice are equivalent resources in Bell experiments

Bell inequalities rest on three fundamental assumptions: realism, locality, and free choice, which lead to nontrivial constraints on correlations in very simple experiments. If we retain realism, then violation of the inequalities implies that at least one of the remaining two assumptions must fail, which can have profound consequences for the causal explanation of the experiment. We investigate the extent to which a given assumption needs to be relaxed for the other to hold at all costs, based on the observation that a violation need not occur on every experimental trial, even when describing correlations violating Bell inequalities. How often this needs to be the case determines the degree of, respectively, locality or free choice in the observed experimental behavior. Despite their disparate character, we show that both assumptions are equally costly. Namely, the resources required to explain the experimental statistics (measured by the frequency of causal interventions of either sort) are exactly the same. Furthermore, we compute such defined measures of locality and free choice for any nonsignaling statistics in a Bell experiment with binary settings, showing that it is directly related to the amount of violation of the so-called Clauser-Horne-Shimony-Holt inequalities. This result is theory independent as it refers directly to the experimental statistics. Additionally, we show how the local fraction results for quantum-mechanical frameworks with infinite number of settings translate into analogous statements for the measure of free choice we introduce. Thus, concerning statistics, causal explanations resorting to either locality or free choice violations are fully interchangeable.

quant-ph↗

arXiv2009

Quantum Probability Explanations for Probability Judgment 'Errors'

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning.

physics.gen-ph↗