36 results on '"Probabilities"'
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2. The Primacy of Doubt : From Quantum Physics to Climate Change, How the Science of Uncertainty Can Help Us Understand Our Chaotic World
- Author
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Tim Palmer and Tim Palmer
- Subjects
- Probabilities, Quantum theory, Weather forecasting, Uncertainty
- Abstract
“Quite possibly the best popular science book I've ever read” (Popular Science) shows how the tools that enabled us to overcome the uncertainty of the weather will enable us to find new answers to modern science's most pressing questions Why does your weather app say “There's a 10% chance of rain” instead of “It will be sunny tomorrow”? In large part this is due to the insight of Tim Palmer, who made uncertainty essential to the study of weather and climate. Now he wants to apply it to how we study everything else. In The Primacy of Doubt, Palmer argues that embracing the mathematics of uncertainty is vital to understanding ourselves and the universe around us. Whether we want to predict climate change or market crashes, understand how the brain is able to outpace supercomputers, or find a theory that links quantum and cosmological physics, Palmer shows how his vision of mathematical uncertainty provides new insights into some of the deepest problems in science. The result is a revolution—one that shows that power begins by embracing what we don't know.
- Published
- 2022
3. Quantum Techniques In Stochastic Mechanics
- Author
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John C Baez, Jacob D Biamonte, John C Baez, and Jacob D Biamonte
- Subjects
- Quantum theory, Stochastic processes, Probabilities
- Abstract
We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets — important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets.
- Published
- 2018
4. Quantum Foundations, Probability and Information
- Author
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Andrei Khrennikov, Bourama Toni, Andrei Khrennikov, and Bourama Toni
- Subjects
- Mathematical physics, Probabilities, Quantum theory
- Abstract
Composed of contributions from leading experts in quantum foundations, this volume presents viewpoints on a number of complex problems through informational, probabilistic, and mathematical perspectives and features novel mathematical models of quantum and subquantum phenomena. Rich with multi-disciplinary mathematical content, this book includes applications of partial differential equations in quantum field theory, differential geometry, oscillatory processes and vibrations, and Feynman integrals for quickly growing potential functions. Due to rapid growth in the field in recent years, this volume aims to promote interdisciplinary collaboration in the areas of quantum probability, information, communication and foundation, and mathematical physics. Many papers discuss complex yet novel problems that depart from the mainstream of quantum physical studies. Others devote explanation to fundamental problems of the conventional quantum theory, including its mathematical formalism. Overall, authors cover a diverse set of topics, including quantum and classical field theory and oscillatory processing, quantum mechanics from a Darwinian evolutionary perspective, and biological applications of quantum theory.Together in one volume, these essays will be useful to experts in the corresponding areas of quantum theory. Theoreticians, experimenters, mathematicians, and even philosophers in quantum physics and quantum probability and information theory can consider this book a valuable resource.
- Published
- 2018
5. Temporal Quantum Correlations and Hidden Variable Models
- Author
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Costantino Budroni and Costantino Budroni
- Subjects
- Probabilities, Quantum theory, Quantum computing
- Abstract
In this thesis, the main approach to the characterization of the set of classical probabilities, the correlation polytope approach, is reviewed for different scenarios, namely, hidden variable models discussed by Bell (local), Kochen and Specker (non-contextual), and Leggett and Garg (macrorealist). Computational difficulties associated with the method are described and a method to overcome them in several nontrivial cases is presented. For the quantum case, a general method to analyze quantum correlations in the sequential measurement scenario is provided, which allows computation of the maximal correlations.Such a method has a direct application for computation of maximal quantum violations of Leggett-Garg inequalities and it is relevant in the analysis of non-contextuality tests. Finally, possible applications of the results for quantum information tasks are discussed.
- Published
- 2016
6. Noncommutative Mathematics for Quantum Systems
- Author
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Uwe Franz, Adam Skalski, Uwe Franz, and Adam Skalski
- Subjects
- Quantum theory, Probabilities, Potential theory (Mathematics)
- Abstract
Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of'making theory noncommutative'has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known'commutative'results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras.
- Published
- 2016
7. Probability And Randomness: Quantum Versus Classical
- Author
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Andrei Yu Khrennikov and Andrei Yu Khrennikov
- Subjects
- Probabilities, Quantum theory, Mathematical physics
- Abstract
Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Probability and Randomness: Quantum versus Classical rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level.
- Published
- 2016
8. Beyond Quantum
- Author
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Andrei Khrennikov and Andrei Khrennikov
- Subjects
- Quantum statistics, Quantum theory, Statistical physics, Probabilities
- Abstract
The present wave of interest in quantum foundations is caused by the tremendous development of quantum information science and its applications to quantum computing and quantum communication. It has become clear that some of the difficulties encountered in realizations of quantum information processing have roots at the very fundamental level. To s
- Published
- 2014
9. Quantum Probability for Probabilists
- Author
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Paul-Andre Meyer and Paul-Andre Meyer
- Subjects
- Probabilities, Quantum theory
- Abstract
These notes contain all the material accumulated over six years in Strasbourg to teach'Quantum Probability'to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabilite8, has been augmented and carefully rewritten, and translated into international English. Still, it remains true'Lecture Notes'material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition'for probabilists'in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than'Quantum Probability', the main topic is'Quantum Stochastic Calculus', a field which has recently got official recognition as 81825 in the Math.
- Published
- 2013
10. The Enigma of Probability and Physics
- Author
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L. Mayants and L. Mayants
- Subjects
- Probabilities, Quantum theory, Statistical mechanics
- Abstract
Lazar Mayants is a recent Russian emigre noted for his work in theoretical physics. He was previously a professor at several universities of the Soviet Union and a distinguished member of the Academy of Sciences of the U.S.S.R, where he worked for about 30 years. In this book he presents a unique, extremely detailed, and embracive version of a subject that has suffered for a long time from numerous internal imperfections. His approach is new and original, the material covered features not only the foundations of the science of probability but also most of its applications, including statistical and quantum mechanics. The key methodolOgical principle underlying the book is of extraordinary significance and deserves special attention. The treatment excels in thoroughness of presentation, in its fulness of mathe matical detail and the abundance of physical examples. The book is intended for a wide range of people interested in probability and its connection with modern science. It is written as a text for advanced students, and I predict that a reader who masters all its contents will become an expert in the subject of both prob ability and its physical implications, while enjoying its understanding and use. HENRY MARGENAU Veritas nihil veretur nisi abscondi (truth'What tremendously easy riddles you ask!'Humpty Dumpty growled out. fears nothing except being hidden). Latin proverb Lewis Carroll, Through the Looking Glass, Chap. 6. Preface The history of producing this book is rather complicated and not quite usual.
- Published
- 2012
11. Ubiquitous Quantum Structure : From Psychology to Finance
- Author
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Andrei Y. Khrennikov and Andrei Y. Khrennikov
- Subjects
- Quantum theory, Probabilities
- Abstract
Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type.
- Published
- 2010
12. Quantum theory of the classical: quantum jumps, Born's Rule and objective classical reality via quantum Darwinism.
- Author
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Zurek, Wojciech Hubert
- Subjects
- *
QUANTUM theory , *EIGHTFOLD way (Nuclear physics) , *HILBERT space - Abstract
The emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists--our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification--of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection. The pointer states obtained in this way determine what can happen--define events--without appealing to Born's Rule for probabilities. Therefore, pk = |ìk|² can now be deduced from the entanglement-assisted invariance, or envariance--a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment--through quantum Darwinism. This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
13. Interpretations of Probability
- Author
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Andrei Khrennikov and Andrei Khrennikov
- Subjects
- p-adic analysis, Quantum theory, Probabilities
- Abstract
This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.
- Published
- 2009
14. Contextual Approach to Quantum Formalism
- Author
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Andrei Y. Khrennikov and Andrei Y. Khrennikov
- Subjects
- Probabilities, Quantum theory
- Abstract
The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell's inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell's theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.
- Published
- 2009
15. Quantum Probability and Spectral Analysis of Graphs
- Author
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Akihito Hora, Nobuaki Obata, Akihito Hora, and Nobuaki Obata
- Subjects
- Graph theory, Quantum theory, Probabilities, Spectrum analysis
- Abstract
It is a great pleasure for me that the new Springer Quantum Probability ProgrammeisopenedbythepresentmonographofAkihitoHoraandNobuaki Obata. In fact this book epitomizes several distinctive features of contemporary quantum probability: First of all the use of speci?c quantum probabilistic techniques to bring original and quite non-trivial contributions to problems with an old history and on which a huge literature exists, both independent of quantum probability. Second, but not less important, the ability to create several bridges among di?erent branches of mathematics apparently far from one another such as the theory of orthogonal polynomials and graph theory, Nevanlinna'stheoryandthetheoryofrepresentationsofthesymmetricgroup. Moreover, the main topic of the present monograph, the asymptotic - haviour of large graphs, is acquiring a growing importance in a multiplicity of applications to several di?erent?elds, from solid state physics to complex networks,frombiologytotelecommunicationsandoperationresearch,toc- binatorialoptimization.Thiscreatesapotentialaudienceforthepresentbook which goes far beyond the mathematicians and includes physicists, engineers of several di?erent branches, as well as biologists and economists. From the mathematical point of view, the use of sophisticated analytical toolstodrawconclusionsondiscretestructures,suchas,graphs,isparticularly appealing. The use of analysis, the science of the continuum, to discover n- trivial properties of discrete structures has an established tradition in number theory, but in graph theory it constitutes a relatively recent trend and there are few doubts that this trend will expand to an extent comparable to what we?nd in the theory of numbers. Two main ideas of quantum probability form theunifying framework of the present book: 1. The quantum decomposition of a classical random variable.
- Published
- 2007
16. Quantum Probability for Probabilists
- Author
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Paul A. Meyer and Paul A. Meyer
- Subjects
- Probabilities, Quantum theory
- Abstract
In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical stochastic calculus and martingale theory, tries to provide an introduction to this rapidly expanding field in a way which should be accessible to probabilists familiar with the Ito integral. It can also, on the other hand, provide a means of access to the methods of stochastic calculus for physicists familiar with Fock space analysis. For this second edition, the author has added about 30 pages of new material, mostly on quantum stochastic integrals.
- Published
- 2006
17. Separation of conditions as a prerequisite for quantum theory
- Subjects
PROBABILITIES ,TERMS ,DERIVATION ,STERN-GERLACH ,Quantum theory ,QUANTIZATION ,MECHANICS ,Separation of conditions ,Logical inference ,Einstein-Podolsky-Rosen-Bohm experiments ,FISHER INFORMATION ,PRINCIPLE ,Stern-Gerlach experiments - Abstract
We introduce the notion of "separation of conditions" meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description depends on mutually exclusive subsets of these conditions. Descriptions that allow a separation of conditions are shown to entail the basic mathematical framework of quantum theory. The Stern-Gerlach and the Einstein-Podolsky-Rosen-Bohm experiment with three, respectively nine possible outcomes are used to illustrate how the separation of conditions can be used to construct their quantum theoretical descriptions. It is shown that the mathematical structure of separated descriptions implies that, under certain restrictions, the time evolution of the data can be described by the von Neumann/Schrodinger equation. (C) 2019 The Authors. Published by Elsevier Inc.
- Published
- 2019
18. Asymptotic Theory Of Quantum Statistical Inference: Selected Papers
- Author
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Masahito Hayashi and Masahito Hayashi
- Subjects
- Quantum theory, Mathematical statistics, Probabilities
- Abstract
Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
- Published
- 2005
19. The Bloch Representation of quantum states.
- Author
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Fargetton, Renan and Arrighi, Pablo
- Subjects
- *
BLOCH constant , *COMPLEX variables , *QUANTUM theory , *QUANTUM scattering , *PROBABILITY theory - Abstract
The Bloch Sphere is widely used as a graphical representation of a qubit. The purpose of this paper is to highlight some new properties of the canonical generalisation of the Bloch Sphere: the Bloch Representation (BR). We give several properties of this representation that makes it a useful representation. We then show the relation between this representation and the probabilities for canonical measurements of the quantum system. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
20. Probability And Schrodinger's Mechanics
- Author
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David B Cook and David B Cook
- Subjects
- Probabilities, Quantum theory
- Abstract
This book addresses some of the problems of interpreting Schrödinger's mechanics — the most complete and explicit theory falling under the umbrella of “quantum theory”. The outlook is materialist (“realist”) and stresses the development of Schrödinger's mechanics from classical theories and its close connections with (particularly) the Hamilton-Jacobi theory. Emphasis is placed on the concepts and use of the modern objective (measure-theoretic) probability theory. The work is free from any mention of the bearing of Schrödinger's mechanics on God, his alleged mind or, indeed, minds at all. The author has taken the naïve view that this mechanics is about the structure and dynamics of atomic and sub-atomic systems since he has been unable to trace any references to minds, consciousness or measurements in the foundations of the theory.
- Published
- 2002
21. From probabilities to mathematical structure of quantum mechanics
- Author
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Kapsa, Vojtěch, Skála, Lubomír, and Chen, Jian
- Subjects
- *
MATHEMATICAL physics , *QUANTUM theory , *DISTRIBUTION (Probability theory) , *WAVE functions , *MOMENTUM (Mechanics) , *FORCE & energy , *POTENTIAL theory (Physics) , *RELATIVITY (Physics) , *EQUATIONS of motion - Abstract
Abstract: A large part of the mathematical formalism of quantum mechanics including the probability density, probability density current, uncertainty relations, wave function, momentum operator, kinetic energy, commutation relations and potentials is related to the probabilistic character of quantum measurements. Equations of motion of quantum mechanics can be obtained from the relativistic invariance of the space–time Fisher information. Some properties of potentials and existence of antiparticles are related to the CPT symmetry. Operators representing parallel or serial physical events in experimental setups can be represented by the sum or product of the corresponding operators. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
- View/download PDF
22. Fine ways to fail to secure local realism
- Author
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Le Bihan, Soazig
- Subjects
- *
BELL'S theorem , *QUANTUM theory , *PHYSICS , *REALISM - Abstract
Abstract: Since he proved his theorem in 1982, Fine has been challenging the traditional interpretation of the experimental violation of the Bell Inequalities (BI). A natural interpretation of Fine''s theorem is that it provides us with an alternative set of assumptions on which to place blame for the failure of the BI, and opens to a new interpretation of the violation of the BI. Fine has a stronger interpretation for his theorem. He claims that his result undermines the traditional interpretation in terms of local realism. The aim of this paper is to understand and to assess Fine''s claim. We distinguish three different strategies that Fine uses in order to support his view. We show that none of these strategies is successful. Fine fails to prove that local realism is not at stake in the violation of the BI by quantum phenomena. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
23. Laws and chances in statistical mechanics
- Author
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Winsberg, Eric
- Subjects
- *
STATISTICAL mechanics , *QUANTUM theory , *PROBABILITY theory , *INTERPRETATION (Philosophy) , *THERMODYNAMICS , *MICROPHYSICS - Abstract
Abstract: Statistical mechanics involves probabilities. At the same time, most approaches to the foundations of statistical mechanics—programs whose goal is to understand the macroscopic laws of thermal physics from the point of view of microphysics—are classical; they begin with the assumption that the underlying dynamical laws that govern the microscopic furniture of the world are (or can without loss of generality be treated as) deterministic. This raises some potential puzzles about the proper interpretation of these probabilities. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
24. On predictions in retro-causal interpretations of quantum mechanics
- Author
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Berkovitz, Joseph
- Subjects
- *
QUANTUM theory , *DISTRIBUTION (Probability theory) , *CAUSALITY (Physics) , *PROBABILITY theory , *CAUSAL models - Abstract
Abstract: The curious correlations between distant events in quantum phenomena suggest the existence of non-local influences. Indeed, as John Bell demonstrated in his celebrated theorem, granted some plausible premises any quantum theory will predict the existence of such non-local influences. One of the theorem''s premises is that the probability distribution of states that systems may assume is independent of the measurements that they undergo at a later time. Retro-causal interpretations of quantum mechanics postulate backward influences from measurement events to the state of systems at an earlier time, and accordingly violate this premise. We argue that retro-causal interpretations predict the existence of closed causal loops, which pose challenges for the predictive and explanatory power of these interpretations. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
25. A SUGGESTIVE WAY OF DERIVING THE QUANTUM PROBABILITY RULE.
- Author
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Sutherland, Roderick
- Abstract
The familiar “modulus squared” form of all quantum mechanical probabilities is derived from an assumption of equal a priori probabilities concerning the final states available. [ABSTRACT FROM AUTHOR]
- Published
- 2000
- Full Text
- View/download PDF
26. Separation of conditions as a prerequisite for quantum theory
- Author
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De Raedt, Hans, Katsnelson, Mikhail I., Willsch, Dennis, Michielsen, Kristel Francine, and Zernike Institute for Advanced Materials
- Subjects
PROBABILITIES ,Quantum Physics ,STERN-GERLACH ,QUANTIZATION ,Logical inference ,FOS: Physical sciences ,TERMS ,DERIVATION ,Quantum theory ,MECHANICS ,Separation of conditions ,Einstein-Podolsky-Rosen-Bohm experiments ,FISHER INFORMATION ,ddc:530 ,PRINCIPLE ,Quantum Physics (quant-ph) ,Stern-Gerlach experiments - Abstract
We introduce the notion of "separation of conditions" meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description depends on mutually exclusive subsets of these conditions. Descriptions that allow a separation of conditions are shown to entail the basic mathematical framework of quantum theory. The Stern-Gerlach and the Einstein-Podolsky-Rosen-Bohm experiment with three, respectively nine possible outcomes are used to illustrate how the separation of conditions can be used to construct their quantum theoretical descriptions. It is shown that the mathematical structure of separated descriptions implies that, under certain restrictions, the time evolution of the data can be described by the von Neumann/Schr\"odinger equation., Comment: Complete rewrite, except for the technical parts. Accepted for publication in Ann. Phys
- Published
- 2019
27. Acerca de una futura explicación transcendental de la probabilidad en mecánica cuántica
- Author
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Pringe, Hernan Bruno
- Subjects
Kant ,Probabilities ,HUMANIDADES ,Regulative laws ,Estudios Religiosos ,Filosofía, Ética y Religión ,Quantum Theory - Abstract
In this paper I put forward some ideas for a future transcendental account of probability in quantum mechanics. Such account will be based on the determination of the epistemological function that probabilistic laws play in quantum mechanics. By means of this determination I expect to take some steps toward a metaphysical foundation of quantum mechanics along Kantian lines, as well as to shed some new light on the current philosophical debate on the notion of probability in quantum mechanics. En este trabajo propongo algunas ideas para una futura explicación trascendental de la probabilidad en mecánica cuántica. Tal explicación se basará en la determinación de la función epistemológica que desempeñan las leyes probabilísticas en mecánica cuántica. Mediante esta determinación espero avanzar hacia una fundamentación metafísica (en sentido kantiano) de la mecánica cuántica, e iluminar el debate actual acerca de la noción de probabilidad en mecánica cuántica. Fil: Pringe, Hernan Bruno. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
- Published
- 2013
28. Probabilities of multiple quantum teleportation
- Author
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Woesler, Richard
- Subjects
Computer Science::Emerging Technologies ,quantum teleportation ,probabilities ,minimal scheme ,Quantum Physics ,quantum theory ,Institut für Verkehrsforschung ,multiple quantum teleportation - Abstract
Using quantum teleportation a quantum state can be teleported with a certain probability. Here the probabilities for multiple teleportation are derived, i. e. for the case that a teleported quantum state is teleported again or even more than two times, for the two-dimensional case, e. g., for the two orthogonal direcations of the polarization of photons. It is shown that the probability for an exact teleportation, except for an irrelevant phase factor, is 25 %, i. e., surprisingly, this result holds for the case of a single teleportation as well as for an arbitrary number of a sequence of teleportations. In the remaining 75 % of the cases, unitary transformations occur, which are equivalent to those occurring for a single teleportation except for an irrelevant phase factor.
- Published
- 2002
29. Extended Statistical Modeling under Symmetry; The Link toward Quantum Mechanics
- Author
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Helland, Inge S.
- Published
- 2006
- Full Text
- View/download PDF
30. Quantum Probability And Related Topics: Volume Viii
- Author
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Luigi Accardi and Luigi Accardi
- Subjects
- Markov processes, Stochastic processes, Probabilities, Quantum theory
- Abstract
Quantum Probability and Related Topics is a series of volumes based on material discussed at the various QP conferences. It aims to provide an update on the rapidly growing field of classical probability, quantum physics and functional analysis.
- Published
- 1993
31. Quantum Probability And Related Topics: Qp-pq (Volume Vi)
- Author
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Luigi Accardi and Luigi Accardi
- Subjects
- Probabilities, Quantum theory
- Abstract
This volume contains several surveys of important developments in quantum probability. The new type of quantum central limit theorems, based on the notion of free independence rather than the usual Boson or Fermion independence is discussed. A surprising result is that the role of the Gaussian for this new type of independence is played by the Wigner distribution. This motivated the introduction of new type of quantum independent increments noise, the free noise and the corresponding stochastic calculus. A further generalization, the ϖ-noises, is discussed. The free stochastic calculus is shown to be able to fit naturally into the general representation free calculus. The basic free are shown to be realized as non-adapted stochastic integrals with respect to the usual Boson white noises. Quantum noise on the finite difference algebra is expressed in terms of the usual Boson white noises. A new quantum way of looking at classical stochastic flows, in particular diffusions on Riemannian Manifolds is explained. Quantum groups are discussed from the point of view of possible applications to quantum probability. The applications of quantum probability to physics are surveyed.
- Published
- 1991
32. Quantum Probability And Related Topics: Qp-pq (Volume Vii)
- Author
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Luigi Accardi and Luigi Accardi
- Subjects
- Quantum theory, Probabilities, Markov processes, Stochastic processes
- Abstract
Quantum Probability and Related Topics is a series of volumes based on materials discussed in the various QP conferences. It aims at providing an update on the rapidly growing field of classical probability, quantum physics and functional analysis.
- Published
- 1992
33. Nature's Capacities and Their Measurement
- Author
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Nancy Cartwright and Nancy Cartwright
- Subjects
- Causality (Physics), Probabilities, Physics--Philosophy, Quantum theory, Econometrics
- Abstract
This book argues for the place of capacities within an grounds of meaning, not method. Yet it is questions of method that should concern the modern empiricist: can capacities be measured? Cartwright argues that they are measured if anything is. Stanford University's Gravity-Probe-B will measure capacities in a cryogenic dewar deep in space. More mundanely, we use probabilities to measure capacities, and the assumptions required to ensure that probabilities are a reliable instrument are investigated in the opening chapters of this book, where the early methods of econometrics set a model. The last chapter applies lessons about probabilities and capacities to quantum mechanics and the Bell inequalities. The central thesis throughout is that capacities not only can be admitted by empiricists, but indeed must be - otherwise the empirical methods of modern science will make no sense.
- Published
- 1989
34. Quantum Probability And Related Topics: Qp-pq (Volume Ix)
- Author
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Luigi Accardi and Luigi Accardi
- Subjects
- Probabilities, Markov processes, Quantum theory, Stochastic processes
- Abstract
Quantum Probability and Related Topics is a series of volumes whose goal is to provide a picture of the state of the art in this rapidly growing field where classical probability, quantum physics and functional analysis merge together in an original synthesis which, for 20 years, has been enriching these three areas with new ideas, techniques and results.
- Published
- 1994
35. Quantum Probability
- Author
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Stanley P. Gudder and Stanley P. Gudder
- Subjects
- Stochastic processes, Multivariate analysis, Statistics, Probabilities, Mathematical physics, Quantum theory
- Abstract
Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism.Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles.The first two chapters survey the necessary background in quantum mechanics and probability theory and therefore the book is fairly self-contained, assuming only an elementary knowledge of linear operators in Hilbert space.
- Published
- 1988
36. Quantum Probability Communications: Volume X
- Author
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R L Hudson, J Martin Lindsay, R L Hudson, and J Martin Lindsay
- Subjects
- Markov processes, Stochastic processes, Probabilities, Quantum theory
- Abstract
Much has changed in the world of quantum probability since the publication of the last volume in this series. Giants in the field, such as P-A Meyer, K R Parthasarathy and W von Waldenfels, have reached the age of retirement. Readers will, however, be pleased to see evidence in the present volume that Partha remains as creatively active as ever. The field itself, regarded at one time as the esoteric province of a small group of devotees, has come of age. It has attracted the enthusiastic commitment of an ever-growing army of young mathematicians and physicists, many of whom are represented here.
- Published
- 1998
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