15 research outputs found
Entanglement as a Method to Reduce Uncertainty
In physics, entanglement 'reduces' the entropy of an entity, because the (von
Neumann) entropy of, e.g., a composite bipartite entity in a pure entangled
state is systematically lower than the entropy of the component sub-entities.
We show here that this 'genuinely non-classical reduction of entropy as a
result of composition' also holds whenever two concepts combine in human
cognition and, more generally, it is valid in human culture. We exploit these
results and make a 'new hypothesis' on the nature of entanglement, namely, the
production of entanglement in the preparation of a composite entity can be seen
as a 'dynamical process of collaboration between its sub-entities to reduce
uncertainty', because the composite entity is in a pure state while its
sub-entities are in a non-pure, or density, state, as a result of the
preparation. We identify within the nature of this entanglement a mechanism of
contextual updating and illustrate the mechanism in the example we analyze. Our
hypothesis naturally explains the 'non-classical nature' of some quantum
logical connectives, as due to Bell-type correlations.Comment: 15 page
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
Spin and Wind Directions I: Identifying Entanglement in Nature and Cognition
We present a cognitive psychology experiment where participants were asked to
select pairs of spatial directions that they considered to be the best example
of 'Two Different Wind Directions'. Data are shown to violate the CHSH version
of Bell's inequality with the same magnitude as in typical Bell-test
experiments with entangled spins. Wind directions thus appear to be conceptual
entities connected through meaning, in human cognition, in a similar way as
spins appear to be entangled in experiments conducted in physics laboratories.
This is the first part of a two-part article. In the second part we present a
symmetrized version of the same experiment for which we provide a quantum
modeling of the collected data in Hilbert space.Comment: The content of the previous article's versions has now been expanded
and reorganized in a two-part article of which this is the first half, the
second half being entitled 'Spin and Wind Directions II: A Bell State Quantum
Model' and to be found at arXiv:1706.0118
Testing Ambiguity and Machina Preferences within a Quantum-theoretic Framework for Decision-making
Quantum-Theoretic Modeling in Computer Science: A Complex Hilbert Space Model for Entangled Concepts in Corpuses of Documents
Testing Ambiguity and Machina Preferences Within a Quantum-theoretic Framework for Decision-making
The Machina thought experiments pose to major non-expected utility models challenges that are similar to those posed by the Ellsberg thought experiments to subjective expected utility theory (SEUT). We test human choices in the `Ellsberg three-color example', confirming typical ambiguity aversion patterns, and the `Machina 50/51 and reflection examples', partially confirming the preferences hypothesized by Machina. Then, we show that a quantum-theoretic framework for decision-making under uncertainty recently elaborated by some of us allows faithful modeling of all data on the Ellsberg and Machina paradox situations. In the quantum-theoretic framework subjective probabilities are represented by quantum probabilities, while quantum state transformations enable representations of ambiguity aversion and subjective attitudes toward it
Quantum-theoretic Modeling in Computer Science: A complex Hilbert space model for entangled concepts in corpuses of documents
We work out a quantum-theoretic model in complex Hilbert space of a recently performed test on co-occurrencies of two concepts and their combination in retrieval processes on specific corpuses of documents. The test violated the Clauser-Horne-Shimony-Holt version of Bellâs inequalities (âCHSH inequalityâ), thus indicating the presence of entanglement between the combined concepts. We make use of a recently elaborated âentanglement schemeâ and represent the collected data in the tensor product of Hilbert spaces of the individual concepts, showing that the identified violation is due to the presence of a strong form of entanglement, involving both states and measurements and reflecting the meaning connection between the component concepts. These results provide a significant confirmation of the presence of quantum structures in corpuses of documents, like it is the case for the entanglement identified in human cognition.<br