12,651 research outputs found
Incompatible Multiple Consistent Sets of Histories and Measures of Quantumness
In the consistent histories (CH) approach to quantum theory probabilities are
assigned to histories subject to a consistency condition of negligible
interference. The approach has the feature that a given physical situation
admits multiple sets of consistent histories that cannot in general be united
into a single consistent set, leading to a number of counter-intuitive or
contrary properties if propositions from different consistent sets are combined
indiscriminately. An alternative viewpoint is proposed in which multiple
consistent sets are classified according to whether or not there exists any
unifying probability for combinations of incompatible sets which replicates the
consistent histories result when restricted to a single consistent set. A
number of examples are exhibited in which this classification can be made, in
some cases with the assistance of the Bell, CHSH or Leggett-Garg inequalities
together with Fine's theorem. When a unifying probability exists logical
deductions in different consistent sets can in fact be combined, an extension
of the "single framework rule". It is argued that this classification coincides
with intuitive notions of the boundary between classical and quantum regimes
and in particular, the absence of a unifying probability for certain
combinations of consistent sets is regarded as a measure of the "quantumness"
of the system. The proposed approach and results are closely related to recent
work on the classification of quasi-probabilities and this connection is
discussed.Comment: 29 pages. Second revised version with discussion of the sample space
and non-uniqueness of the unifying probability and small errors correcte
Quantum Structure in Cognition, Origins, Developments, Successes and Expectations
We provide an overview of the results we have attained in the last decade on
the identification of quantum structures in cognition and, more specifically,
in the formalization and representation of natural concepts. We firstly discuss
the quantum foundational reasons that led us to investigate the mechanisms of
formation and combination of concepts in human reasoning, starting from the
empirically observed deviations from classical logical and probabilistic
structures. We then develop our quantum-theoretic perspective in Fock space
which allows successful modeling of various sets of cognitive experiments
collected by different scientists, including ourselves. In addition, we
formulate a unified explanatory hypothesis for the presence of quantum
structures in cognitive processes, and discuss our recent discovery of further
quantum aspects in concept combinations, namely, 'entanglement' and
'indistinguishability'. We finally illustrate perspectives for future research.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1412.870
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