29 found
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  1. What is Shannon information?Olimpia Lombardi, Federico Holik & Leonardo Vanni - 2016 - Synthese 193 (7):1983-2012.
    Despite of its formal precision and its great many applications, Shannon’s theory still offers an active terrain of debate when the interpretation of its main concepts is the task at issue. In this article we try to analyze certain points that still remain obscure or matter of discussion, and whose elucidation contribute to the assessment of the different interpretative proposals about the concept of information. In particular, we argue for a pluralist position, according to which the different views about information (...)
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  2. Q-spaces and the Foundations of Quantum Mechanics.Graciela Domenech, Federico Holik & Décio Krause - 2008 - Foundations of Physics 38 (11):969-994.
    Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build (...)
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  3.  88
    A Discussion on Particle Number and Quantum Indistinguishability.Graciela Domenech & Federico Holik - 2007 - Foundations of Physics 37 (6):855-878.
    The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schrödinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first-order language using quasiset theory (Q). In this work, we (...)
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  4.  48
    Quasi-set theory: a formal approach to a quantum ontology of properties.Federico Holik, Juan Pablo Jorge, Décio Krause & Olimpia Lombardi - 2022 - Synthese 200 (5):1-26.
    In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate meta-language to speak of the proposed ontology of properties and its structure.
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  5. 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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  6.  19
    Ontological indistinguishability as a central tenet of quantum theory.José Acacio de Barros & Federico Holik - 2023 - Philosophical Transactions of the Royal Society A 381:20220100.
    Quantum indistinguishability directly relates to the philosophical debate on the notions of identity and individuality. They are crucial for our understanding of multipartite quantum systems. Furthermore, the correct interpretation of this feature of quantum theory has implications that transcend fundamental science and philosophy, given that quantum indistinguishability is a resource in quantum information theory. Most of the conceptual analysis of quantum indistinguishability is restricted to studying the permutational invariance of quantum states, the concomitant quantum statistics and their entanglement. Here, we (...)
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  7.  80
    What is quantum information?Olimpia Lombardi, Federico Holik & Leonardo Vanni - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 56:17-26.
    In the present paper we develop different arguments to show that there are no reasons to consider that there exists quantum information as qualitatively different than Shannon information. There is only one kind of information, which can be coded by means of orthogonal or non-orthogonal states. The analogy between Shannon’s theory and Schumacher’s theory is confined to coding theorems. The attempt to extend the analogy beyond this original scope leads to a concept of quantum information that becomes indistinguishable from that (...)
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  8. 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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  9.  69
    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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  10.  35
    A formal framework for the study of the notion of undefined particle number in quantum mechanics.Federico Holik & Newton C. A. da Costa - 2015 - Synthese 192 (2):505-523.
    It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of (...)
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  11.  82
    A formal framework for the study of the notion of undefined particle number in quantum mechanics.Newton C. A. da Costa & Federico Holik - 2015 - Synthese 192 (2):505-523.
    It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of (...)
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  12.  44
    Open Problems in the Development of a Quantum Mereology.Federico Holik & Juan Pablo Jorge - 2023 - In Jonas R. B. Arenhart & Raoni W. Arroyo (eds.), Non-Reflexive Logics, Non-Individuals, and the Philosophy of Quantum Mechanics: Essays in Honour of the Philosophy of Décio Krause. Springer Verlag. pp. 157-176.
    Mereology deals with the study of the relations between wholes and parts. In this work we will discuss different developments and open problems related to the formulation of a quantum mereology. In particular, we will discuss different advances in the development of formal systems aimed to describe the whole-parts relationship in the context of quantum theory.
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  13. 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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  14.  6
    A Logical Approach to the Quantum-to-Classical Transition.Sebastian Fortin, Manuel Gadella, Federico Holik & Marcelo Losada - 2019 - In Olimpia Lombardi (ed.), Quantum Worlds: Perspectives on the Ontology of Quantum Mechanics. New York, NY: Cambridge University Press. pp. 360 - 378.
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  15.  77
    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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  16. 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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  17.  37
    Pattern Recognition in Non-Kolmogorovian Structures.Federico Holik, Giuseppe Sergioli, Hector Freytes & Angelo Plastino - 2018 - Foundations of Science 23 (1):119-132.
    We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which obey probabilistic laws which do not comply with Kolmogorov’s axioms. We show that such a scenario accommodates many important examples, and in particular, we provide a rigorous definition of the classical and the quantum pattern recognition problems, respectively. Our framework allows for the introduction of (...)
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  18.  9
    Non-unitary evolution of quantum logics.Sebastian Fortin, Federico Holik & Leonardo Vanni - 2016 - In F. Bagarello, R. Passante & C. Trapani (eds.), Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. pp. 219-234.
    In this work we present a dynamical approach to quantum logics. By changing the standard formalism of quantum mechanics to allow non-Hermitian operators as generators of time evolution, we address the question of how can logics evolve in time. In this way, we describe formally how a non-Boolean algebra may become a Boolean one under certain conditions. We present some simple models which illustrate this transition and develop a new quantum logical formalism based in complex spectral resolutions, a notion that (...)
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  19. 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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  20. 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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  21. Identity, Individuality and Indistinguishability in Physics and Mathematics.Gabriel Catren & Federico Holik (eds.) - 2023 - London: Philosophical Transactions Of The Royal Society A.
    Can there be two things that are completely indistinguishable? This simple question has raised numerous debates throughout the history of philosophy and science. The principle of the identity of indiscernibles claims that no two things can be completely indiscernible. But this thesis has been challenged in quantum physics and continues to be a hot topic in cutting edge areas of mathematics. The question has gained a renewed interest with the possibility of harnessing indistinguishability as a resource in quantum information tasks. (...)
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  22. Quantum identity, content, and context: from classical to non-classical logic.José Acacio de Barros, Federico Holik & Décio Krause - 2022 - In Shyam Wuppuluri & Ian Stewart (eds.), From Electrons to Elephants and Elections: Exploring the Role of Content and Context. Springer Nature.
     
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  23.  25
    Classical limit and quantum logic.Marcelo Losada, Sebastian Fortin & Federico Holik - 2018 - International Journal of Theoretical Physics 57:465–475.
    The more common scheme to explain the classical limit of quantum mechanics includes decoherence, which removes from the state the interference terms classically inadmissible since embodying non-Booleanity. In this work we consider the classical limit from a logical viewpoint, as a quantum-to-Boolean transition. The aim is to open the door to a new study based on dynamical logics, that is, logics that change over time. In particular, we appeal to the notion of hybrid logics to describe semiclassical systems. Moreover, we (...)
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  24.  28
    A new conceptual scheme for the interpretation of the improper mixtures in quantum mechanics.Federico Holik, Christian de Ronde & Wim Christiaens - 2013 - Scientiae Studia 11 (1):101-118.
    En este artículo, analizamos el significado de las matrices densidad en el formalismo de la mecánica cuántica. Discutimos el problema de los "sistemas cuánticos compuestos" en la lógica cuántica así como también la interpretación de las mezclas impropias. Tomando en cuenta el desarrollo de la lógica cuántica convexa, presentamos un análisis de la estructura formal de la teoría que, argumentaremos, debe ser considerado a la hora de desarrollar un nuevo esquema conceptual para la interpretación de las mezclas cuánticas. In this (...)
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  25. Classical models for quantum information.Federico Holik & Gustavo Martin Bosyk - 2017 - In Olimpia Lombardi, Sebastian Fortin, Federico Holik & Cristian López (eds.), What is Quantum Information? New York, NY: CUP.
     
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  26.  19
    On the interpretation of probabilities in generalized probabilistic models.Federico Holik, Sebastian Fortin, Gustavo Bosyk & Angelo Plastino - 2016 - In José Acacio de Barros, Bob Coecke & E. Pothos (eds.), Quantum Interaction. QI 2016. Lecture Notes in Computer Science, Vol. 10106. Springer, Cham. pp. 194-205.
    We discuss generalized pobabilistic models for which states not necessarily obey Kolmogorov's axioms of probability. We study the relationship between properties and probabilistic measures in this setting, and explore some possible interpretations of these measures.
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  27.  39
    Quantum Logical Structures For Identical Particles.Federico Holik, Krause Decio & Gómez Ignacio - 2016 - Cadernos de História E Filosofia da Ciéncia 2 (1):13-58.
    In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of indistinguishable particles, and draw possible philosophical implications. We also review some proposals available in the literature (...)
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  28. Prefacio.Décio Krause & Federico Holik - 2019 - Metatheoria – Revista de Filosofía E Historia de la Ciencia 9:1.
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  29.  13
    What is Quantum Information?Olimpia Lombardi, Sebastian Fortin, Federico Holik & Cristian López (eds.) - 2017 - New York, NY: CUP.
    Combining physics and philosophy, this is a uniquely interdisciplinary examination of quantum information science. Suitable as both a discussion of the conceptual and philosophical problems of this field and a comprehensive stand-alone introduction, this book will benefit both experienced and new researchers in quantum information and the philosophy of physics.
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