probability and randomness quantum versus classical

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Probability And Randomness

Author : Andrei Khrennikov
ISBN : 9781783267989
Genre : Mathematics
File Size : 86. 53 MB
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' 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. Contents:Foundations of ProbabilityRandomnessSupplementary Notes on Measure-theoretic and Frequency ApproachesIntroduction to Quantum FormalismQuantum and Contextual ProbabilityInterpretations of Quantum Mechanics and ProbabilityRandomness: Quantum Versus ClassicalProbabilistic Structure of Bell''s ArgumentQuantum Probability Outside of Physics: from Molecular Biology to Cognition Readership: Researchers in mathematical physics, probability and statistics. Keywords:Kolmogorov Axiomataics;Randomness;Independence;Quantum Probability'

Quantum Computing Since Democritus

Author : Scott Aaronson
ISBN : 9780521199568
Genre : Computers
File Size : 83. 26 MB
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Takes students and researchers on a tour through some of the deepest ideas of maths, computer science and physics.

Quantum Chance

Author : Nicolas Gisin
ISBN : 9783319054735
Genre : Science
File Size : 85. 24 MB
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Quantum physics, which offers an explanation of the world on the smallest scale, has fundamental implications that pose a serious challenge to ordinary logic. Particularly counterintuitive is the notion of entanglement, which has been explored for the past 30 years and posits an ubiquitous randomness capable of manifesting itself simultaneously in more than one place. This amazing 'non-locality' is more than just an abstract curiosity or paradox: it has entirely down-to-earth applications in cryptography, serving for example to protect financial information; it also has enabled the demonstration of 'quantum teleportation', whose infinite possibilities even science-fiction writers can scarcely imagine. This delightful and concise exposition does not avoid the deep logical difficulties of quantum physics, but gives the reader the insights needed to appreciate them. From 'Bell's Theorem' to experiments in quantum entanglement, the reader will gain a solid understanding of one of the most fascinating areas of contemporary physics.

Einstein S Dreams

Author : Alan Lightman
ISBN : 9780307789747
Genre : Fiction
File Size : 56. 63 MB
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A modern classic, Einstein’s Dreams is a fictional collage of stories dreamed by Albert Einstein in 1905, about time, relativity and physics. As the defiant but sensitive young genius is creating his theory of relativity, a new conception of time, he imagines many possible worlds. In one, time is circular, so that people are fated to repeat triumphs and failures over and over. In another, there is a place where time stands still, visited by lovers and parents clinging to their children. In another, time is a nightingale, sometimes trapped by a bell jar. Now translated into thirty languages, Einstein’s Dreams has inspired playwrights, dancers, musicians, and painters all over the world. In poetic vignettes, it explores the connections between science and art, the process of creativity, and ultimately the fragility of human existence.

Quantum Adaptivity In Biology From Genetics To Cognition

Author : Masanari Asano
ISBN : 9789401798198
Genre : Science
File Size : 44. 12 MB
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This book examines information processing performed by bio-systems at all scales: from genomes, cells and proteins to cognitive and even social systems. It introduces a theoretical/conceptual principle based on quantum information and non-Kolmogorov probability theory to explain information processing phenomena in biology as a whole. The book begins with an introduction followed by two chapters devoted to fundamentals, one covering classical and quantum probability, which also contains a brief introduction to quantum formalism, and another on an information approach to molecular biology, genetics and epigenetics. It then goes on to examine adaptive dynamics, including applications to biology, and non-Kolmogorov probability theory. Next, the book discusses the possibility to apply the quantum formalism to model biological evolution, especially at the cellular level: genetic and epigenetic evolutions. It also presents a model of the epigenetic cellular evolution based on the mathematical formalism of open quantum systems. The last two chapters of the book explore foundational problems of quantum mechanics and demonstrate the power of usage of positive operator valued measures (POVMs) in biological science. This book will appeal to a diverse group of readers including experts in biology, cognitive science, decision making, sociology, psychology, and physics; mathematicians working on problems of quantum probability and information and researchers in quantum foundations.

An Introduction To Quantum Computing

Author : Phillip Kaye
ISBN : 9780198570004
Genre : Computers
File Size : 89. 55 MB
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The authors provide an introduction to quantum computing. Aimed at advanced undergraduate and beginning graduate students in these disciplines, this text is illustrated with diagrams and exercises.

Interpretations Of Probability

Author : Andrei Khrennikov
ISBN : 9783110213195
Genre : Mathematics
File Size : 80. 16 MB
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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.

The Physics Of Star Trek

Author : Lawrence M. Krauss
ISBN : 9780465008636
Genre : Science
File Size : 60. 96 MB
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What warps when you're traveling at warp speed? What is the difference between a wormhole and a black hole? Are time loops really possible, and can I kill my grandmother before I am born? Anyone who has ever wondered “could this really happen?” will gain useful insights into the Star Trek universe (and, incidentally, the real world of physics) in this charming and accessible guide. Lawrence M. Krauss boldly goes where Star Trek has gone-and beyond. From Newton to Hawking, from Einstein to Feynman, from Kirk to Picard, Krauss leads readers on a voyage to the world of physics as we now know it and as it might one day be.

Probability Theory

Author : E. T. Jaynes
ISBN : 9781139435161
Genre : Science
File Size : 38. 73 MB
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The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.

Understanding Quantum Mechanics

Author : Roland Omnès
ISBN : 0691004358
Genre : Science
File Size : 67. 50 MB
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Here Roland Omn�s offers a clear, up-to-date guide to the conceptual framework of quantum mechanics. In an area that has provoked much philosophical debate, Omn�s has achieved high recognition for his Interpretation of Quantum Mechanics (Princeton 1994), a book for specialists. Now the author has transformed his own theory into a short and readable text that enables beginning students and experienced physicists, mathematicians, and philosophers to form a comprehensive picture of the field while learning about the most recent advances. This new book presents a more streamlined version of the Copenhagen interpretation, showing its logical consistency and completeness. The problem of measurement is a major area of inquiry, with the author surveying its history from Planck to Heisenberg before describing the consistent-histories interpretation. He draws upon the most recent research on the decoherence effect (related to the modern resolution of the famous Schr�dinger's cat problem) and an exact formulation of the correspondence between quantum and particle physics (implying a derivation of classical determinism from quantum probabilism). Interpretation is organized with the help of a universal and sound language using so-called consistent histories. As a language and a method, it can now be shown to be free of ambiguity and it makes interpretation much clearer and closer to common sense.

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