7 research outputs found
Quantum Entanglement in Concept Combinations
Research in the application of quantum structures to cognitive science
confirms that these structures quite systematically appear in the dynamics of
concepts and their combinations and quantum-based models faithfully represent
experimental data of situations where classical approaches are problematical.
In this paper, we analyze the data we collected in an experiment on a specific
conceptual combination, showing that Bell's inequalities are violated in the
experiment. We present a new refined entanglement scheme to model these data
within standard quantum theory rules, where 'entangled measurements and
entangled evolutions' occur, in addition to the expected 'entangled states',
and present a full quantum representation in complex Hilbert space of the data.
This stronger form of entanglement in measurements and evolutions might have
relevant applications in the foundations of quantum theory, as well as in the
interpretation of nonlocality tests. It could indeed explain some
non-negligible 'anomalies' identified in EPR-Bell experiments.Comment: 16 pages, no figure
Quantum entanglement in physical and cognitive systems: a conceptual analysis and a general representation
We provide a general description of the phenomenon of entanglement in
bipartite systems, as it manifests in micro and macro physical systems, as well
as in human cognitive processes. We do so by observing that when genuine
coincidence measurements are considered, the violation of the 'marginal laws',
in addition to the Bell-CHSH inequality, is also to be expected. The situation
can be described in the quantum formalism by considering the presence of
entanglement not only at the level of the states, but also at the level of the
measurements. However, at the "local'" level of a specific joint measurement, a
description where entanglement is only incorporated in the state remains always
possible, by adopting a fine-tuned tensor product representation. But
contextual tensor product representations should only be considered when there
are good reasons to describe the outcome-states as (non-entangled) product
states. This will not in general be true, hence, the entangement resource will
have to generally be allocated both in the states and in the measurements. In
view of the numerous violations of the marginal laws observed in physics'
laboratories, it remains unclear to date if entanglement in micro-physical
systems is to be understood only as an 'entanglement of the states', or also as
an 'entanglement of the measurements'. But even if measurements would also be
entangled, the corresponding violation of the marginal laws (no-signaling
conditions) would not for this imply that a superluminal communication would be
possible
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Bell correlations outside physics
Correlations are ubiquitous in nature and their principled study is of paramount importance in scientific development. The seminal contributions from John Bell offer a framework for analyzing the correlations between the components of quantum mechanical systems and have instigated an experimental tradition which has recently culminated with the Nobel Prize in Physics (2022). In physics, Bell’s framework allows the demonstration of the non-classical nature of quantum systems just from the analysis of the observed correlation patterns. Bell’s ideas need not be restricted to physics. Our contribution is to show an example of a Bell approach, based on the insight that correlations can be broken down into a part due to common, ostensibly significant causes, and a part due to noise. We employ data from finance (price changes of securities) as an example to demonstrate our approach, highlighting several general applications: first, we demonstrate a new measure of association, informed by the assumed causal relationship between variables. Second, our framework can lead to streamlined Bell-type tests of widely employed models of association, which are in principle applicable to any discipline. In the area of finance, such models of association are Factor Models and the bivariate Gaussian model. Overall, we show that Bell’s approach and the models we consider are applicable as general statistical techniques, without any domain specificity. We hope that our work will pave the way for extending our general understanding for how the structure of associations can be analyzed
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A Quantum Approach to Human Decision Making
This thesis examines various aspects of decision making, with a focus on probabilistic tools to cognitive modeling. One such tool is the so-called Classical Probability Theory (CPT, or Bayesian Theory; Tenenbaum & Griffiths, 2001; Chater et al., 2006), which has been the dominant approach in understanding different aspects of human behavior. The broad argument is that cognitive processing must reflect some kind of optimal adaptation to environmental statistical structure and, therefore, human cognition must be consistent with the principles of CPT (Oaksford & Chater, 2009). CPT indeed appears to provide accurate descriptions of behavior in many cases, particularly decision making (Siegel et al., 2018), which is the focus of this work