Results for 'Quantum probability theory'

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  1. Quantum Probability Theory.Miklós Rédei & Stephen Jeffrey Summers - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):390-417.
  2.  36
    Critical Reflections on Quantum Probability Theory.László Szabó - 2001 - Vienna Circle Institute Yearbook 8:201-219.
    The story of quantum probability theory and quantum logic begins with von Neumann’s recognition1, that quantum mechanics can be regarded as a kind of “probability theory”, if the subspace lattice L of the system’s Hilbert space H plays the role of event algebra and the ‘tr’-s play the role of probability distributions over these events. This idea had been completed in the Gleason theorem 2.
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  3.  18
    Quantum Probability Theory as a Common Framework for Reasoning and Similarity.Jennifer S. Trueblood, Emmanuel M. Pothos & Jerome R. Busemeyer - 2014 - Frontiers in Psychology 5.
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    Comments on Quantum Probability Theory.Steven Sloman - 2014 - Topics in Cognitive Science 6 (1):47-52.
    Quantum probability theory (QP) is the best formal representation available of the most common form of judgment involving attribute comparison (inside judgment). People are capable, however, of judgments that involve proportions over sets of instances (outside judgment). Here, the theory does not do so well. I discuss the theory both in terms of descriptive adequacy and normative appropriateness.
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  5.  13
    Analysis of Quantum Probability Theory. I.James Van Aken - 1985 - Journal of Philosophical Logic 14 (3):267-296.
  6.  21
    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).
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  7. 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 (...)
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  8. Analysis of Quantum Probability Theory. II.James Aken - 1986 - Journal of Philosophical Logic 15 (3):333 - 367.
  9.  72
    Quantum Probability and Decision Theory, Revisited [2002 Online-Only Paper].David Wallace - 2002
    An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented which are based upon different decision theories and upon Gleason's Theorem. It is argued that decision theory gives Everettians most or all of what they need from `probability'. Contact is made with Lewis's Principal Principle linking subjective credence with objective chance: an (...)
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  10. Analysis of Quantum Probability Theory. I.James Aken - 1985 - Journal of Philosophical Logic 14 (3):267 - 296.
  11. Characterizing Common Cause Closedness of Quantum Probability Theories.Yuichiro Kitajima & Miklós Rédei - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (B):234-241.
    We prove new results on common cause closedness of quantum probability spaces, where by a quantum probability space is meant the projection lattice of a non-commutative von Neumann algebra together with a countably additive probability measure on the lattice. Common cause closedness is the feature that for every correlation between a pair of commuting projections there exists in the lattice a third projection commuting with both of the correlated projections and which is a Reichenbachian common (...)
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  12. 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 (...)
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  13.  11
    Analysis of Quantum Probability Theory. II.James van Aken - 1986 - Journal of Philosophical Logic 15 (3):333-367.
  14. Kolmogorovian Censorship Hypothesis For General Quantum Probability Theories.MiklÓs RÉdei - 2010 - Manuscrito 33 (1):365-380.
    It is shown that the Kolmogorovian Censorship Hypothesis, according to which quantum probabilities are interpretable as conditional probabilities in a classical probability measure space, holds not only for Hilbert space quantum mechanics but for general quantum probability theories based on the theory of von Neumann algebras.
     
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  15.  49
    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 (...)
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  16.  69
    Realistic Neurons Can Compute the Operations Needed by Quantum Probability Theory and Other Vector Symbolic Architectures.Terrence C. Stewart & Chris Eliasmith - 2013 - Behavioral and Brain Sciences 36 (3):307 - 308.
    Quantum probability (QP) theory can be seen as a type of vector symbolic architecture (VSA): mental states are vectors storing structured information and manipulated using algebraic operations. Furthermore, the operations needed by QP match those in other VSAs. This allows existing biologically realistic neural models to be adapted to provide a mechanistic explanation of the cognitive phenomena described in the target article by Pothos & Busemeyer (P&B).
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  17.  10
    Quantum Probability Quantum Logic.Itamar Pitowsky - 1989 - 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 (...)
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  18.  44
    Processes Models, Environmental Analyses, and Cognitive Architectures: Quo Vadis Quantum Probability Theory?Julian N. Marewski & Ulrich Hoffrage - 2013 - Behavioral and Brain Sciences 36 (3):297 - 298.
    A lot of research in cognition and decision making suffers from a lack of formalism. The quantum probability program could help to improve this situation, but we wonder whether it would provide even more added value if its presumed focus on outcome models were complemented by process models that are, ideally, informed by ecological analyses and integrated into cognitive architectures.
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  19.  42
    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 (...)
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  20.  39
    Interpreting Probabilities in Quantum Field Theory and Quantum Statistical Mechanics.Laura Ruetsche & John Earman - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 263.
    Philosophical accounts of quantum theory commonly suppose that the observables of a quantum system form a Type-I factor von Neumann algebra. Such algebras always have atoms, which are minimal projection operators in the case of quantum mechanics. However, relativistic quantum field theory and the thermodynamic limit of quantum statistical mechanics make extensive use of von Neumann algebras of more general types. This chapter addresses the question whether interpretations of quantum probability devised (...)
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  21.  71
    On the Strong Law of Large Numbers in Quantum Probability Theory.W. Ochs - 1977 - Journal of Philosophical Logic 6 (1):473 - 480.
  22.  52
    Quantum Probability and the Foundations of Quantum Theory.Luigi Accardi - 1990 - In Roger Cooke & Domenico Costantini (eds.), Boston Studies in the Philosophy of Science. Springer Verlag. pp. 119-147.
    The point of view advocated, in the last ten years, by quantum probability about the foundations of quantum mechanics, is based on the investigation of the mathematical consequences of a deep and elementary idea developed by the founding fathers of quantum mechanics and accepted nowadays as a truism by most physicists, namely: one should be careful when applying the rules derived from the experience of macroscopic physics to experiments which are mutually incompatible in the sense of (...)
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  23. On the Strong Law of Large Numbers in Quantum Probability Theory.P. Mittelstaedt - 1977 - Journal of Philosophical Logic 6 (4):473.
  24.  6
    Probability Theories in General and Quantum Theory in Particular.Lucién Hardy - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):381-393.
  25.  32
    Quantum Logic and Probability Theory.Alexander Wilce - 2008 - Stanford Encyclopedia of Philosophy.
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  26.  16
    Processes Models, Environmental Analyses, and Cognitive Architectures: Quo Vadis Quantum Probability Theory?—ERRATUM.Julian N. Marewski & Ulrich Hoffrage - 2013 - Behavioral and Brain Sciences 36 (4):463-463.
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  27. Bell’s Theorem, Quantum Probabilities, and Superdeterminism.Eddy Keming Chen - 2021 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. Routledge.
    In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.
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  28. 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 (...) calculus for QM/sets. The point is not to clarify finite probability theory but to elucidate quantum mechanics itself by seeing some of its quantum features in a classical setting. (shrink)
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  29.  94
    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.
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  30. 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 (...)
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  31. Quantum Mechanics and Classical Probability Theory.Joseph D. Sneed - 1970 - Synthese 21 (1):34 - 64.
  32.  59
    Quantum Mechanics Over Sets: A Pedagogical Model with Non-Commutative Finite Probability Theory as its Quantum Probability Calculus.David Ellerman - 2017 - Synthese (12):4863-4896.
    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 have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and (...)
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  33. Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability.Itamar Pitowsky - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):395-414.
    We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance, the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, (...)
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  34.  25
    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. (...)
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  35. Non-Monotonic Probability Theory for N-State Quantum Systems.Fred Kronz - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2):259-272.
    In previous work, a non-standard theory of probability was formulated and used to systematize interference effects involving the simplest type of quantum systems. The main result here is a self-contained, non-trivial generalization of that theory to capture interference effects involving a much broader range of quantum systems. The discussion also focuses on interpretive matters having to do with the actual/virtual distinction, non-locality, and conditional probabilities.
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  36.  11
    Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability.Itamar Pitowsky - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):395-414.
    We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in (...)
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  37.  21
    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.
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  38.  30
    Generalized Quantum Probability and Entanglement Enhancement Witnessing.Gregg Jaeger - 2012 - Foundations of Physics 42 (6):752-759.
    It has been suggested (cf. Sinha et al. in Science 329:418, 2010) that the Born rule for quantum probability could be violated. It has also been suggested that, in a generalized version of quantum mechanical probability theory such as that proposed by Sorkin (Mod. Phys. Lett. A 9:3119, 1994) there might occur deviations from the predictions of quantum probability in cases where more than two paths are available to a self-interfering system. These would (...)
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  39.  50
    Quantum Probability and Operational Statistics.Stanley Gudder - 1990 - Foundations of Physics 20 (5):499-527.
    We develop the concept of quantum probability based on ideas of R. Feynman. The general guidelines of quantum probability are translated into rigorous mathematical definitions. We then compare the resulting framework with that of operational statistics. We discuss various relationship between measurements and define quantum stochastic processes. It is shown that quantum probability includes both conventional probability theory and traditional quantum mechanics. Discrete quantum systems, transition amplitudes, and discrete Feynman (...)
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  40. Can Quantum Mechanics Be Formulated as a Classical Probability Theory?Leon Cohen - 1966 - Philosophy of Science 33 (4):317-322.
    It is shown that quantum mechanics cannot be formulated as a stochastic theory involving a probability distribution function of position and momentum. This is done by showing that the most general distribution function which yields the proper quantum mechanical marginal distributions cannot consistently be used to predict the expectations of observables if phase space integration is used. Implications relating to the possibility of establishing a "hidden" variable theory of quantum mechanics are discussed.
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  41. Quantum Logic and Generalized Probability Theory.P. Mittelstaedt - 1977 - Journal of Philosophical Logic 6 (4):455.
  42.  42
    Formal Problems of Probability Theory in the Light of Quantum Mechanics III.M. Strauss - 1939 - Synthese 4 (12):65 - 72.
    (1) The form of scientific probability sentences is given unambiguously for the first time by quantum mechanics (form (II); all scientific probability statements can be written in this form. (2) The rules of transformation are also determined by quantum mechanics they agree with the axioms given by Reichenbach (1), p. 118. (3) Frequency interpretation agreeing with the statistical tests used in scientific practice can be given in the frame of truth-semantics at least aa a first approximation.
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  43.  89
    Quantum Theory: A Hilbert Space Formalism for Probability Theory.R. Eugene Collins - 1977 - Foundations of Physics 7 (7-8):475-494.
    It is shown that the Hilbert space formalism of quantum mechanics can be derived as a corrected form of probability theory. These constructions yield the Schrödinger equation for a particle in an electromagnetic field and exhibit a relationship of this equation to Markov processes. The operator formalism for expectation values is shown to be related to anL 2 representation of marginal distributions and a relationship of the commutation rules for canonically conjugate observables to a topological relationship of (...)
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  44.  80
    Some Remarks on Classical Probability Theory in Quantum Mechanics.G. Gerlich - 1981 - Erkenntnis 16 (3):335 - 338.
  45. Quantum Logic, Quantum Probability, and Quantum Measurement: A Philosophical Perspective on the Quantum Theory.Donald Richard Nilson - 1972 - Dissertation, Indiana University
     
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  46.  81
    Spacetime Quantum Probabilities, Relativized Descriptions, and Popperian Propensities. Part I: Spacetime Quantum Probabilities. [REVIEW]Mioara Mugur-Schächter - 1991 - Foundations of Physics 21 (12):1387-1449.
    An integrated view concerning the probabilistic organization of quantum mechanics is obtained by systematic confrontation of the Kolmogorov formulation of the abstract theory of probabilities, with the quantum mechanical representationand its factual counterparts. Because these factual counterparts possess a peculiar spacetime structure stemming from the operations by which the observer produces the studied states (operations of state preparation) and the qualifications of these (operations of measurement), the approach brings forth “probability trees,” complex constructs with treelike spacetime (...)
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  47. Probability Theory with Superposition Events.David Ellerman - manuscript
    In finite probability theory, events are subsets S⊆U of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation (...)
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  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 (...)
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  49.  27
    Quantum Logic and Generalized Probability Theory.U. Kägi-Romano - 1977 - Journal of Philosophical Logic 6 (1):455 - 462.
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    Formal Problems of Probability Theory in the Light of Quantum Mechanics I.M. Strauss - 1938 - Synthese 3 (12):35 - 40.
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