1,720,970 research outputs found
Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability
No full textWe 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, even in such finite gambles. These include the uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics to it. We conclude with a philosophical discussion on the interpretation of quantum mechanics
Quantum mechanics as a theory of probability
Get PDFWe develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it. The construction proceeds in the following steps: (a) Axioms for the algebra of events are introduced following Birkhoff and von Neumann. All axioms, except the one that expresses the uncertainty principle, are shared with the classical event space. The only models for the set of axioms are lattices of subspaces of inner product spaces over a field K. (b) Another axiom due to Soler forces K to be the field of real, or complex numbers, or the quaternions. We suggest a probabilistic reading of Soler's axiom. (c) Gleason's theorem fully characterizes the probability measures on the algebra of events, so that Born's rule is derived. (d) Gleason's theorem is equivalent to the existence of a certain finite set of rays, with a particular orthogonality graph (Wondergraph). Consequently, all aspects of quantum probability can be derived from rational probability assignments to finite "quantum gambles". (e) All experimental aspects of entanglement- the violation of Bell's inequality in particular- are explained as natural outcomes of the probabilistic structure. (f) We hypothesize that even in the absence of decoherence macroscopic entanglement can very rarely be observed, and provide a precise conjecture to that effect .We also discuss the relation of the present approach to quantum logic, realism and truth, and the measurement problem
Random Witnesses and the Classical Character of Macroscopic Objects
Get PDFWhy don't we see large macroscopic objects in entangled states? Even if the particles composing the object were all entangled and insulated from the environment, we shall still find it almost always impossible to observe the superposition. The reason is that as the number of particles n grows, we need an ever more careful preparation, and an ever more carefully designed experiment, in order to recognize the entangled character of the state of the object. An observable W that distinguishes all the unentangled states from some entangled states is called a witness. We consider witnesses on n quantum bits (qbits), and use the following normalization: A witness W satisfies |tr(Wr)|1, with the norm being the maximum among the absolute values of the eigenvalues of W. Although there are n-qbit witnesses whose norm is exponential in n, we conjecture that for a large majority of such witnesses ||W||<=O[(nlogn)^1/2]. We prove this conjecture for the family of extremal witnesses introduced by Werner and Wolf (Phys. Rev. A 64, 032112 (2001)). Assuming the conjecture is valid we argue that multiparticle entanglement can be detected only if a system has been carefully prepared in a very special state. Otherwise, multiparticle entanglement lies below the threshold of detection, even if it exists, and even if decoherence has been ``turned off''
Physical theory and its interpretation: essays in honor of Jeffrey Bub
No full textThe essays in this volume were written by leading researchers on classical mechanics, statistical mechanics, quantum theory and relativity. The papers cover a number of central topics in the foundations of physics, including the role of symmetry principles in classical and quantum physics (papers by Butterfield and by Healey), Einstein's hole argument in general relativity (Korte), quantum mechanics and special relativity (Hemmo and Berkovitz, Brown and Timpson), quantum correlations (Glymour, Redei), quantum logic (Demopoulos, Isham, Stairs), and quantum probability and information (Gudder,
Quantum probability - quantum logic /
No full textThis volume, that is intended as a research monograph on the conceptual foundations of quantum mechanics, shows new ways of investigation of quantum mechanical problems. At its center is the concept of correlation as it appears in probability theory and quantum physics. It is closely related to and characterizes the possible range of values of quantum correlations, Bell-type inequalities in the Einstein-Podolsky-Rosen experiment, and classical and quantum propositional logic, mentioning only some of the notably questions. The subject has applications in studying problems outside of physics, too. The book includes a detailed construction of local hidden variable theories, based on an extension of classical probability.Bibliography: p. [197]-209.This volume, that is intended as a research monograph on the conceptual foundations of quantum mechanics, shows new ways of investigation of quantum mechanical problems. At its center is the concept of correlation as it appears in probability theory and quantum physics. It is closely related to and characterizes the possible range of values of quantum correlations, Bell-type inequalities in the Einstein-Podolsky-Rosen experiment, and classical and quantum propositional logic, mentioning only some of the notably questions. The subject has applications in studying problems outside of physics, too. The book includes a detailed construction of local hidden variable theories, based on an extension of classical probability
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
- …
