8 found
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  1. On the Connection Between Quantum Probability and Geometry.Federico Holik - 2021 - Quanta 10 (1):1-14.
    We discuss the mathematical structures that underlie quantum probabilities. More specifically, we explore possible connections between logic, geometry and probability theory. We propose an interpretation that generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories. We stress the relevance of developing a geometrical interpretation of quantum mechanics.
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  2. Non-Kolmogorovian Probabilities and Quantum Technologies.Federico Holik - 2023 - Entropy 24 (11):1666.
    In this work, we focus on the philosophical aspects and technical challenges that underlie the axiomatization of the non-Kolmogorovian probability framework, in connection with the problem of quantum contextuality. This fundamental feature of quantum theory has received a lot of attention recently, given that it might be connected to the speed-up of quantum computers—a phenomenon that is not fully understood. Although this problem has been extensively studied in the physics community, there are still many philosophical questions that should be properly (...)
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    An Approach to QST-based Nmatrices Semantics.Juan Pablo Jorge, Federico Holik & Décio Krause - 2023 - Principia: An International Journal of Epistemology 27 (3):539-607.
    This paper introduces the theory QST of quasets as a formal basis for the Nmatrices. The main aim is to construct a system of Nmatrices by substituting standard sets by quasets. Since QST is a conservative extension of ZFA (the Zermelo-Fraenkel set theory with Atoms), it is possible to obtain generalized Nmatrices (Q-Nmatrices). Since the original formulation of QST is not completely adequate for the developments we advance here, some possible amendments to the theory are also considered. One of the (...)
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  4. A discussion on the origin of quantum probabilities.Federico Holik, Manuel Sáenz & Angelo Plastino - 2014 - Annals of Physics 340 (1):293-310.
    We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).
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  5.  67
    Lógica cuántica, Nmatrices y adecuación, I (3rd edition).Juan Pablo Jorge & Federico Holik - 2022 - Teorema: International Journal of Philosophy 41 (3):65-88.
    In this paper we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics. We give a characterization of the degree of non-functionality which is compatible with the propositional structure of quantum theory, showing that having truth-functional connectives, together with some assumptions regarding the relation of logical consequence, commits us to the adequacy of the interpretation sets of these connectives. An advantage of our proof is that it is independent of (...)
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  6. Indistinguishability and the origins of contextuality in physics.José Acacio De Barros, Federico Holik & Décio Krause - 2019 - Philosophical Transactions of the Royal Society A 377 (2157): 20190150.
    In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This framework allows us to consider a new ontology (...)
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  7. Logic, Geometry And Probability Theory.Federico Holik - 2013 - SOP Transactions On Theoretical Physics 1:128 - 137.
    We discuss the relationship between logic, geometry and probability theory under the light of a novel approach to quantum probabilities which generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories.
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  8. Contextuality and Indistinguishability.Acacio de Barros, Federico Holik & Décio Krause - 2017 - Entropy 19 ((9)):435.
    It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default, sheaf theory, topos theory, and non-standard or signed probabilities. In this paper we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties (...)
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