1,736 research outputs found
Bell-type inequalities for bivariate maps on orthomodular lattices
Bell-type inequalities on orthomodular lattices, in which conjunctions of
propositions are not modeled by meets but by maps for simultaneous measurements
(s-maps), are studied. It is shown that the most simple of these inequalities,
that involves only two propositions, is always satisfied, contrary to what
happens in the case of traditional version of this inequality in which
conjunctions of propositions are modeled by meets. Equivalence of various
Bell-type inequalities formulated with the aid of bivariate maps on
orthomodular lattices is studied. Our invesigations shed new light on the
interpretation of various multivariate maps defined on orthomodular lattices
already studied in the literature. The paper is concluded by showing the
possibility of using s-maps and j-maps to represent counterfactual conjunctions
and disjunctions of non-compatible propositions about quantum systems.Comment: 14 pages, no figure
Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought
We analyze different aspects of our quantum modeling approach of human
concepts, and more specifically focus on the quantum effects of contextuality,
interference, entanglement and emergence, illustrating how each of them makes
its appearance in specific situations of the dynamics of human concepts and
their combinations. We point out the relation of our approach, which is based
on an ontology of a concept as an entity in a state changing under influence of
a context, with the main traditional concept theories, i.e. prototype theory,
exemplar theory and theory theory. We ponder about the question why quantum
theory performs so well in its modeling of human concepts, and shed light on
this question by analyzing the role of complex amplitudes, showing how they
allow to describe interference in the statistics of measurement outcomes, while
in the traditional theories statistics of outcomes originates in classical
probability weights, without the possibility of interference. The relevance of
complex numbers, the appearance of entanglement, and the role of Fock space in
explaining contextual emergence, all as unique features of the quantum
modeling, are explicitly revealed in this paper by analyzing human concepts and
their dynamics.Comment: 31 pages, 5 figure
Faking quantum probabilities: Beyond Bell's theorem and Tsirelson bounds
Local hidden-variable model of singlet-state correlations discussed in M.
Czachor, Arithmetic loophole in Bell's Theorem: Overlooked threat to
entangled-state quantum cryptography, Acta Phys. Polon. A 139, 70-83 (2021), is
shown to be a particular case of an infinite hierarchy of local hidden-variable
models based on an infinite hierarchy of calculi. Violation of Bell-type
inequalities is shown to be a `confusion of languages' problem, a result of
mixing different but neighboring levels of the hierarchy. Mixing of
non-neighboring levels results in violations beyond the Tsirelson bounds.Comment: A talk related to this paper can be watched at
https://www.youtube.com/watch?v=W5z8HfIltO
Unsharp Quantum Reality
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way
EPR Paradox,Locality and Completeness of Quantum Theory
The quantum theory (QT) and new stochastic approaches have no deterministic
prediction for a single measurement or for a single time -series of events
observed for a trapped ion, electron or any other individual physical system.
The predictions of QT being of probabilistic character apply to the statistical
distribution of the results obtained in various experiments. The probability
distribution is not an attribute of a dice but it is a characteristic of a
whole random experiment : '' rolling a dice''. and statistical long range
correlations between two random variables X and Y are not a proof of any causal
relation between these variable. Moreover any probabilistic model used to
describe a random experiment is consistent only with a specific protocol
telling how the random experiment has to be performed.In this sense the quantum
theory is a statistical and contextual theory of phenomena. In this paper we
discuss these important topics in some detail. Besides we discuss in historical
perspective various prerequisites used in the proofs of Bell and CHSH
inequalities concluding that the violation of these inequalities in spin
polarization correlation experiments is neither a proof of the completeness of
QT nor of its nonlocality. The question whether QT is predictably complete is
still open and it should be answered by a careful and unconventional analysis
of the experimental data. It is sufficient to analyze more in detail the
existing experimental data by using various non-parametric purity tests and
other specific statistical tools invented to study the fine structure of the
time-series. The correct understanding of statistical and contextual character
of QT has far reaching consequences for the quantum information and quantum
computing.Comment: 16 pages, 59 references,the contribution to the conference QTRF-4
held in Vaxjo, Sweden, 11-16 june 2007. To be published in the Proceeding
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