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Author: V. P. Belavkin
Publisher: World Scientific
ISBN: 9812832963
Category : Science
Languages : en
Pages : 410
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Book Description
Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems.This volume contains a selection of regular research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability and quantum information. The selection offers a unified view of recent trends in quantum stochastics, highlighting the common mathematical language of Hilbert space operators, and the deep connections between classical and quantum stochastic phenomena.
Author: V. P. Belavkin
Publisher: World Scientific
ISBN: 9812832963
Category : Science
Languages : en
Pages : 410
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Book Description
Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems.This volume contains a selection of regular research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability and quantum information. The selection offers a unified view of recent trends in quantum stochastics, highlighting the common mathematical language of Hilbert space operators, and the deep connections between classical and quantum stochastic phenomena.
Author: Viacheslav P Belavkin
Publisher: World Scientific
ISBN: 981451828X
Category : Science
Languages : en
Pages : 410
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Book Description
Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems.This volume contains a selection of regular research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability and quantum information. The selection offers a unified view of recent trends in quantum stochastics, highlighting the common mathematical language of Hilbert space operators, and the deep connections between classical and quantum stochastic phenomena.
Author: Mou-Hsiung Chang
Publisher: Cambridge University Press
ISBN: 1316195120
Category : Mathematics
Languages : en
Pages : 425
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Book Description
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigroups and processes, and large-time asymptotic behavior of quantum Markov semigroups.
Author: Masahito Hayashi
Publisher: Springer
ISBN: 3662497255
Category : Computers
Languages : en
Pages : 672
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Book Description
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions.
Author: Luigi Accardi
Publisher: Springer Science & Business Media
ISBN: 3662049295
Category : Science
Languages : en
Pages : 485
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Book Description
Well suited as a textbook in the emerging field of stochastic limit, which is a new mathematical technique developed for solving nonlinear problems in quantum theory.
Author: John C Baez
Publisher: World Scientific
ISBN: 981322696X
Category : Science
Languages : en
Pages : 276
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Book Description
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.
Author: K.R. Parthasarathy
Publisher: Birkhäuser
ISBN: 3034886411
Category : Mathematics
Languages : en
Pages : 299
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Book Description
"Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly "This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle. Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields. Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.
Author: Hendra I Nurdin
Publisher: Springer
ISBN: 3319552015
Category : Technology & Engineering
Languages : en
Pages : 273
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Book Description
This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics will find this book to be a valuable treatment of the control of an important class of quantum systems. The material presented here will also interest physicists working in optics, quantum optics, quantum information theory and other quantum-physical disciplines.
Author: Harish Parthasarathy
Publisher: CRC Press
ISBN: 1000373487
Category : Science
Languages : en
Pages : 319
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Book Description
This book is about several questions regarding how to describe the quantization of the current density in an antenna and about the nature of the quantum electromagnetic field produced by such a quantum current density. The second quantized current density can be built out of the Dirac field of electrons and positrons while the free electromagnetic or photon field is built out of solutions to the wave equation with coefficients being operators, namely the creation and annihilation operators of the photons. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
Author: Rolando Rebolledo
Publisher: World Scientific
ISBN: 9814338745
Category : Mathematics
Languages : en
Pages : 339
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Book Description
This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
