Results for 'Classical and quantum probability'

976 found
Order:
  1.  20
    Additivity Requirements in Classical and Quantum Probability.John Earman - unknown
    The discussion of different principles of additivity for probability functions has been largely focused on the personalist interpretation of probability. Very little attention has been given to additivity principles for physical probabilities. The form of additivity for quantum probabilities is determined by the algebra of observables that characterize a physical system and the type of quantum state that is realizable and preparable for that system. We assess arguments designed to show that only normal quantum states (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  2. General causal propensities, classical and quantum probabilities.David Sapire - 1992 - Philosophical Papers 21 (3):243-258.
  3.  10
    The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus.Andrei Khrennikov, Irina Basieva, Eric Guerci, Sébastien Duchêne & Ismaël Rafaï - 2021 - Theory and Decision 92 (2):387-406.
    Recently quantum probability theory started to be actively used in studies of human decision-making, in particular for the resolution of paradoxes (such as the Allais, Ellsberg, and Machina paradoxes). Previous studies were based on a cognitive metaphor of the quantum double-slit experiment—the basic quantum interference experiment. In this paper, we report on an economics experiment based on a triple-slit experiment design, where the slits are menus of alternatives from which one can choose. The test of nonclassicality (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  4. Logical Entropy: Introduction to Classical and Quantum Logical Information theory.David Ellerman - 2018 - Entropy 20 (9):679.
    Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  5. On Classical and Quantum Logical Entropy.David Ellerman - manuscript
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  6.  50
    Stochastic theory for classical and quantum mechanical systems.L. de la Peña & A. M. Cetto - 1975 - Foundations of Physics 5 (2):355-370.
    We formulate from first principles a theory of stochastic processes in configuration space. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schrödinger equation, which is derived here (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  7. Probability Description and Entropy of Classical and Quantum Systems.Margarita A. Man’ko & Vladimir I. Man’ko - 2011 - Foundations of Physics 41 (3):330-344.
    Tomographic approach to describing both the states in classical statistical mechanics and the states in quantum mechanics using the fair probability distributions is reviewed. The entropy associated with the probability distribution (tomographic entropy) for classical and quantum systems is studied. The experimental possibility to check the inequalities like the position–momentum uncertainty relations and entropic uncertainty relations are considered.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  8. CHSH Inequality: Quantum Probabilities as Classical Conditional Probabilities.Andrei Khrennikov - 2015 - Foundations of Physics 45 (7):711-725.
    In this note we demonstrate that the results of observations in the EPR–Bohm–Bell experiment can be described within the classical probabilistic framework. However, the “quantum probabilities” have to be interpreted as conditional probabilities, where conditioning is with respect to fixed experimental settings. Our approach is based on the complete account of randomness involved in the experiment. The crucial point is that randomness of selections of experimental settings has to be taken into account within one consistent framework covering all (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  9.  91
    Picturing classical and quantum Bayesian inference.Bob Coecke & Robert W. Spekkens - 2012 - Synthese 186 (3):651 - 696.
    We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  10.  30
    The Twofold Role of Observables in Classical and Quantum Kinematics.Federico Zalamea - 2018 - Foundations of Physics 48 (9):1061-1091.
    Observables have a dual nature in both classical and quantum kinematics: they are at the same time quantities, allowing to separate states by means of their numerical values, and generators of transformations, establishing relations between different states. In this work, we show how this twofold role of observables constitutes a key feature in the conceptual analysis of classical and quantum kinematics, shedding a new light on the distinguishing feature of the quantum at the kinematical level. (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  11.  24
    The Twofold Role of Observables in Classical and Quantum Kinematics.Federico Zalamea - 2018 - Foundations of Physics 48 (9):1061-1091.
    Observables have a dual nature in both classical and quantum kinematics: they are at the same time quantities, allowing to separate states by means of their numerical values, and generators of transformations, establishing relations between different states. In this work, we show how this twofold role of observables constitutes a key feature in the conceptual analysis of classical and quantum kinematics, shedding a new light on the distinguishing feature of the quantum at the kinematical level. (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  12.  33
    Atomism Today. Classical and Quantum Concepts of Elementary Particles.Andrzej Łukasik - 2008 - Dialogue and Universalism 18 (11-12):31-38.
    Atomism is the programme explaining all changes in terms of invariant units. The development of physics during the 20th century may be treated as a spectacular triumph of atomism. However, paradoxically, changes and conceptual difficulties brought about by quantum mechanics lead to the conclusion that the ontological model provided by classical atomism has become inadequate. Atoms (and elementary particles) are not atomos—indivisible, perfectly solid, unchangeable, ungenerated and indestructible (eternal), and the void is not simply an empty space. According (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  13. On the nature of continuous physical quantities in classical and quantum mechanics.Hans Halvorson - 2001 - Journal of Philosophical Logic 30 (1):27-50.
    Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No - that the status of individual continuous quantities is very different in quantum mechanics than (...)
    Direct download (14 more)  
     
    Export citation  
     
    Bookmark   23 citations  
  14. Quantum, Probability, Logic: Itamar Pitowsky’s Work and Influence.Meir Hemmo & Orly Shenker (eds.) - 2020 - Springer.
    This volume provides a broad perspective on the state of the art in the philosophy and conceptual foundations of quantum mechanics. Its essays take their starting point in the work and influence of Itamar Pitowsky, who has greatly influenced our understanding of what is characteristically non-classical about quantum probabilities and quantum logic, and this serves as a vantage point from which they reflect on key ongoing debates in the field. Readers will find a definitive and multi-faceted (...)
    No categories
     
    Export citation  
     
    Bookmark  
  15. A Quantum Probability Account of Order Effects in Inference.Jennifer S. Trueblood & Jerome R. Busemeyer - 2011 - Cognitive Science 35 (8):1518-1552.
    Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains (...)
    Direct download  
     
    Export citation  
     
    Bookmark   25 citations  
  16.  18
    Probability implication in the logics of classical and quantum mechanics.Sŀawomir Bugajski - 1978 - Journal of Philosophical Logic 7 (1):95 - 106.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  17. Can quantum probability provide a new direction for cognitive modeling?Emmanuel M. Pothos & Jerome R. Busemeyer - 2013 - Behavioral and Brain Sciences 36 (3):255-274.
    Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   55 citations  
  18.  21
    From Classical to Quantum Models: The Regularising Rôle of Integrals, Symmetry and Probabilities.Jean-Pierre Gazeau - 2018 - Foundations of Physics 48 (11):1648-1667.
    In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like “point” particle, motion “on the line”, “smooth” observables, wave function, and even “going to infinity”, without forgetting perplexing phrases like “classical world” versus “quantum world”.... On the other hand, when a mathematical model becomes really inoperative in regard with correct predictions, one is forced to replace it with (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  19.  24
    If quantum probability = classical probability + bounded cognition; is this good, bad, or unnecessary?Tim Rakow - 2013 - Behavioral and Brain Sciences 36 (3):304-305.
    Quantum probability models may supersede existing probabilistic models because they account for behaviour inconsistent with classical probability theory that are attributable to normal limitations of cognition. This intriguing position, however, may overstate weaknesses in classical probability theory by underestimating the role of current knowledge states and may under-employ available knowledge about the limitations of cognitive processes. In addition, flexibility in model specification has risks for the use of quantum probability.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  20.  51
    Quantum probability and unified approach to quantization and dynamics.Blagowest A. Nikolov - 1996 - Foundations of Physics 26 (2):257-269.
    A simplified derivation of the Gudder-Hemion quantum probability formula is proposed. Defining configurations as the classical (q, p) deterministic states and generalized action as the (quantum) generating function of a canonical transformation, we obtain the usual quantization rules (for arbitrary polynomial quantities) and derive the Schrödinger wave equation on the same grounds. This approach suggests a statistical interpretation of the wave function in terms of the classical canonical transformations.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  21.  37
    Quantum probability and comparative cognition.Randolph C. Grace & Simon Kemp - 2013 - Behavioral and Brain Sciences 36 (3):287-287.
    Evolution would favor organisms that can make recurrent decisions in accordance with classical probability (CP) theory, because such choices would be optimal in the long run. This is illustrated by the base-rate fallacy and probability matching, where nonhumans choose optimally but humans do not. Quantum probability (QP) theory may be able to account for these species differences in terms of orthogonal versus nonorthogonal representations.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  22.  34
    Quantum probability, intuition, and human rationality.Mike Oaksford - 2013 - Behavioral and Brain Sciences 36 (3):303-303.
    This comment suggests that Pothos & Busmeyer (P&B) do not provide an intuitive rational foundation for quantum probability (QP) theory to parallel standard logic and classical probability (CP) theory. In particular, the intuitive foundation for standard logic, which underpins CP, is the elimination of contradictions – that is, believing p and not-p is bad. Quantum logic, which underpins QP, explicitly denies non-contradiction, which seems deeply counterintuitive for the macroscopic world about which people must reason. I (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  23.  34
    Quantum probability and cognitive modeling: Some cautions and a promising direction in modeling physics learning.Donald R. Franceschetti & Elizabeth Gire - 2013 - Behavioral and Brain Sciences 36 (3):284-285.
    Quantum probability theory offers a viable alternative to classical probability, although there are some ambiguities inherent in transferring the quantum formalism to a less determined realm. A number of physicists are now looking at the applicability of quantum ideas to the assessment of physics learning, an area particularly suited to quantum probability ideas.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  24. Probability and quantum foundation.Han Geurdes - manuscript
    A classical probabilistics explanation for a typical quantum effect in Hardy's paradox is demonstrated.
    Direct download  
     
    Export citation  
     
    Bookmark  
  25. A Quantum Probability Perspective on Borderline Vagueness.Reinhard Blutner, Emmanuel M. Pothos & Peter Bruza - 2013 - Topics in Cognitive Science 5 (4):711-736.
    The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  26.  28
    Quantum ProbabilityQuantum Logic.Itamar Pitowsky - 2014 - Springer.
    This book compares various approaches to the interpretation of quantum mechanics, in particular those which are related to the key words "the Copenhagen interpretation", "the antirealist view", "quantum logic" and "hidden variable theory". Using the concept of "correlation" carefully analyzed in the context of classical probability and in quantum theory, the author provides a framework to compare these approaches. He also develops an extension of probability theory to construct a local hidden variable theory. The (...)
    Direct download  
     
    Export citation  
     
    Bookmark   52 citations  
  27. Quantum probability and many worlds.Meir Hemmo - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):333-350.
    We discuss the meaning of probabilities in the many worlds interpretation of quantum mechanics. We start by presenting very briefly the many worlds theory, how the problem of probability arises, and some unsuccessful attempts to solve it in the past. Then we criticize a recent attempt by Deutsch to derive the quantum mechanical probabilities from the nonprobabilistic parts of quantum mechanics and classical decision theory. We further argue that the Born probability does not make (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  28.  34
    Is quantum probability rational?Alasdair I. Houston & Karoline Wiesner - 2013 - Behavioral and Brain Sciences 36 (3):291 - 292.
    We concentrate on two aspects of the article by Pothos & Busemeyer (P&B): the relationship between classical and quantum probability and quantum probability as a basis for rational decisions. We argue that the mathematical relationship between classical and quantum probability is not quite what the authors claim. Furthermore, it might be premature to regard quantum probability as the best practical rational scheme for decision making.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  29.  60
    Quantum probability, choice in large worlds, and the statistical structure of reality.Don Ross & James Ladyman - 2013 - Behavioral and Brain Sciences 36 (3):305-306.
    Classical probability models of incentive response are inadequate in where the dimensions of relative risk and the dimensions of similarity in outcome comparisons typically differ. Quantum probability models for choice in large worlds may be motivated pragmatically or metaphysically: statistical processing in the brain adapts to the true scale-relative structure of the universe.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  30. On classical finite probability theory as a quantum probability calculus.David Ellerman - manuscript
    This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  31.  84
    The concept of a proposition in classical and quantum physics.Robin Giles - 1979 - Studia Logica 38 (4):337 - 353.
    A proposition is associated in classical mechanics with a subset of phase space, in quantum logic with a projection in Hilbert space, and in both cases with a 2-valued observable or test. A theoretical statement typically assigns a probability to such a pure test. However, since a pure test is an idealization not realizable experimentally, it is necessary — to give such a statement a practical meaning — to describe how it can be approximated by feasible tests. (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  32.  65
    The concept of indistinguishable particles in classical and quantum physics.Alexander Bach - 1988 - Foundations of Physics 18 (6):639-649.
    The consequences of the following definition of indistinguishability are analyzed. Indistinguishable classical or quantum particles are identical classical or quantum particles in a state characterized by a probability measure, a statistical operator respectively, which is invariant under any permutation of the particles. According to this definition the particles of classical Maxwell-Boltzmann statistics are indistinguishable.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  33.  80
    On the Reasonable and Unreasonable Effectiveness of Mathematics in Classical and Quantum Physics.Arkady Plotnitsky - 2011 - Foundations of Physics 41 (3):466-491.
    The point of departure for this article is Werner Heisenberg’s remark, made in 1929: “It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  34.  60
    The Relation between Credence and Chance: Lewis' "Principal Principle" Is a Theorem of Quantum Probability Theory.John Earman - unknown
    David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. Given the generally accepted updating rule for quantum probabilities, there is a straight forward sense (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  35.  52
    Probability theories in general and quantum theory in particular.L. Hardy - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):381-393.
    We consider probability theories in general. In the first part of the paper, various constraints are imposed and classical probability and quantum theory are recovered as special cases. Quantum theory follows from a set of five reasonable axioms. The key axiom which gives us quantum theory rather than classical probability theory is the continuity axiom, which demands that there exists a continuous reversible transformation between any pair of pure states. In the second (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  36. Quantum mechanics and operational probability theory.E. G. Beltrametti & S. Bugajski - 2002 - Foundations of Science 7 (1-2):197-212.
    We discuss a generalization of the standard notion of probability space and show that the emerging framework, to be called operational probability theory, can be considered as underlying quantal theories. The proposed framework makes special reference to the convex structure of states and to a family of observables which is wider than the familiar set of random variables: it appears as an alternative to the known algebraic approach to quantum probability.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  37.  68
    Quantum Probability: An Introduction.Guido Bacciagaluppi - unknown
    The topic of probabilty in quantum mechanics is rather vast, and in this article, we shall choose to discuss it from the perspective of whether and in what sense quantum mechanics requires a generalisation of the usual concept of probability. We shall focus on the case of finite-dimensional quantum mechanics, partly for simplicity and partly for ease of generalisation. While we shall largely focus on formal aspects of quantum probability, our discussion will relate also (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  38. Range theorems for quantum probability and entanglement.Itamar Pitowsky - unknown
    We consider the set of all matrices of the form pij = tr[W (Ei ⊗ Fj)] where Ei, Fj are projections on a Hilbert space H, and W is some state on H ⊗ H. We derive the basic properties of this set, compare it with the classical range of probability, and note how its properties may be related to a geometric measures of entanglement.
     
    Export citation  
     
    Bookmark   3 citations  
  39. Logic, probability, and quantum theory.Arthur I. Fine - 1968 - Philosophy of Science 35 (2):101-111.
    The aim of this paper is to present and discuss a probabilistic framework that is adequate for the formulation of quantum theory and faithful to its applications. Contrary to claims, which are examined and rebutted, that quantum theory employs a nonclassical probability theory based on a nonclassical "logic," the probabilistic framework set out here is entirely classical and the "logic" used is Boolean. The framework consists of a set of states and a set of quantities that (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  40.  23
    Beyond quantum probability: Another formalism shared by quantum physics and psychology.Ehtibar N. Dzhafarov & Janne V. Kujala - 2013 - Behavioral and Brain Sciences 36 (3):283 - 284.
    There is another meeting place for quantum physics and psychology, both within and outside of cognitive modeling. In physics it is known as the issue of classical (probabilistic) determinism, and in psychology it is known as the issue of selective influences. The formalisms independently developed in the two areas for dealing with these issues turn out to be identical, opening ways for mutually beneficial interactions.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  41.  45
    Philosophy of Quantum Probability - An empiricist study of its formalism and logic.Ronnie Hermens - unknown
    The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  42. Open Parallel Cooperative and Competitive Decision Processes: A Potential Provenance for Quantum Probability Decision Models.Ian G. Fuss & Daniel J. Navarro - 2013 - Topics in Cognitive Science 5 (4):818-843.
    In recent years quantum probability models have been used to explain many aspects of human decision making, and as such quantum models have been considered a viable alternative to Bayesian models based on classical probability. One criticism that is often leveled at both kinds of models is that they lack a clear interpretation in terms of psychological mechanisms. In this paper we discuss the mechanistic underpinnings of a quantum walk model of human decision making (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  43. Operationism, probability and quantum mechanics.Maria Carla Galavotti - 1995 - Foundations of Science 1 (1):99-118.
    This paper investigates the kind of empiricism combined with an operationalist perspective that, in the first decades of our Century, gave rise to a turning point in theoretical physics and in probability theory. While quantum mechanics was taking shape, the classical (Laplacian) interpretation of probability gave way to two divergent perspectives: frequentism and subjectivism. Frequentism gained wide acceptance among theoretical physicists. Subjectivism, on the other hand, was never held to be a serious candidate for application to (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  44.  33
    Relational Quantum Mechanics and Probability.M. Trassinelli - 2018 - Foundations of Physics 48 (9):1092-1111.
    We present a derivation of the third postulate of relational quantum mechanics from the properties of conditional probabilities. The first two RQM postulates are based on the information that can be extracted from interaction of different systems, and the third postulate defines the properties of the probability function. Here we demonstrate that from a rigorous definition of the conditional probability for the possible outcomes of different measurements, the third postulate is unnecessary and the Born’s rule naturally emerges (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  45.  29
    Cold and hot cognition: Quantum probability theory and realistic psychological modeling.Philip J. Corr - 2013 - Behavioral and Brain Sciences 36 (3):282 - 283.
    Typically, human decision making is emotionally and does not conform to classical probability (CP) theory. As quantum probability (QP) theory emphasises order, context, superimposition states, and nonlinear dynamic effects, one of its major strengths may be its power to unify formal modeling and realistic psychological theory (e.g., information uncertainty, anxiety, and indecision, as seen in the Prisoner's Dilemma).
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  46.  27
    An Epistemic Interpretation of Quantum Probability via Contextuality.Claudio Garola - 2020 - Foundations of Science 25 (1):105-120.
    According to a standard view, quantum mechanics is a contextual theory and quantum probability does not satisfy Kolmogorov’s axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the microscopic contexts underlying them, that one can interpret quantum probability as epistemic, despite its non-Kolmogorovian structure. To attain this result we introduce a predicate language L, a classical probability measure on it and a family of classical probability measures on (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  47.  74
    Mechanics: Non-classical, Non-quantum.Elliott Tammaro - 2012 - Foundations of Physics 42 (2):284-290.
    A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of interest for two primary reasons. Firstly, NCQs arise prominently in semi-classical approximation schemes. Their formal study may yield improved approximation techniques in the near-classical regime. More importantly for the purposes of this note, it may be possible for NCQs to reproduce (...) results over experimentally tested regimes while having a well defined classical limit, and hence are viable alternative theories. We illustrate an NCQ by considering an explicit class of NCQ mechanics. Here this class will be arrived at via a natural generalization of classical mechanics formulated in terms of a probability density functional. (shrink)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  48. Quantum probability in logical space.John C. Bigelow - 1979 - Philosophy of Science 46 (2):223-243.
    Probability measures can be constructed using the measure-theoretic techniques of Caratheodory and Hausdorff. Under these constructions one obtains first an outer measure over "events" or "propositions." Then, if one restricts this outer measure to the measurable propositions, one finally obtains a classical probability theory. What I argue is that outer measures can also be used to yield the structures of probability theories in quantum mechanics, provided we permit them to range over at least some unmeasurable (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  49. Measurements and quantum states: Part II.Henry Margenau - 1963 - Philosophy of Science 30 (2):138-157.
    This is the second, mathematically more detailed part of a paper consisting of two articles, the first having appeared in the immediately preceding issue of this Journal. It shows that a measurement converts a pure case into a mixture with reducible probabilities. The measurement as such permits no inference whatever as to the state of the physical system subjected to measurement after the measurement has been performed. But because the probabilities after the act are classical and therefore reducible, it (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   14 citations  
  50.  46
    Four and a Half Axioms for Finite-Dimensional Quantum Probability.Alexander Wilce - 2012 - In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. pp. 281--298.
    It is an old idea, lately out of fashion but now experiencing a revival, that quantum mechanics may best be understood, not as a physical theory with a problematic probabilistic interpretation, but as something closer to a probability calculus per se. However, from this angle, the rather special C *-algebraic apparatus of quantum probability theory stands in need of further motivation. One would like to find additional principles, having clear physical and/or probabilistic content, on the basis (...)
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
1 — 50 / 976