Luigi Accardi

Wolfgang Freudenberg

Masanori Ohya

The purpose of this proceedings volume is to return to the starting point of bio-informatics and quantum information, fields that are growing rapidly at present, and to seriously attempt mutual interaction between the two, with a view to enumerating and solving the many fundamental problems they entail. For such a purpose, we look for interdisciplinary bridges in mathematics, physics, information and life sciences, in particular, research for new paradigm for information science and life science on the basis of quantum theory.

Quantum Bioinformatics Four

Wilhelm v. Waldenfels

This volume, the fourth of the quantum probability series, collects part of the contributions to the Year of Quantum Probability organized by the Volterra Center of University of Rome II. The intensive communication among researchers during this Year allowed several open problems to be solved and several inexpected connections to be revealed.

Proceedings of the Year of Quantum Probability, held at the University of Rome II, Italy, 1987

Quantum Probability and Applications IV

The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers. Contents: Coherent Quantum Control of -Atoms Through the Stochastic Limit (L Accardi); Information, Innovation and Elemental Random Field (T Hida); Joint Extension of States of Fermion Subsystems (H Araki); Emergence of White Noise Equations from Classical Quantum Mechanics (A Boukas); Saturation of an Entropy Bound and Quantum Markov States (D Petz); Quantum Entanglement, Purification, and Linear-Optics Quantum Gates with Photonic Qubits (P Walther & A Zeilinger); Group Theory of Dynamical Maps (E C G Sudarshan); Quantum Logical Gates Realized by Beam Splittings (W Freudenberg et al.); Generalized Sectors and Adjunctions (I Ojima); Note on Quantum Mutual Type Measures and Capacity (N Watanabe); Structure of Linear Processes (S Si); An Infinite Dimensional Laplacian Acting on Some Class of Levy White Noise Functionals (K Saito); Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H Fichtner et al.); Noncanonical Representations of a Multi-Dimensional Brownian Motion (Y Hibino); and other papers. Readership: Researchers in quantum physics and theoretical physics.

Quantum Information and Computing

Si Si

Noboru Watanabe

This volume aims to return to the starting point of the fields of infinite dimensional analysis and quantum probability, fields that are growing rapidly at present, and to seriously attempt mutual interaction between the two, with a view to enumerating and solving the many fundamental problems they entail. For such a purpose, we look for interdisciplinary bridges in mathematics including classical probability and to different branches of physics, in particular, research for new paradigms for information science on the basis of quantum theory.

Infinite Dimensional Analysis, Quantum Probability And Related Topics, Qp38 - Proceedings Of The International Conference

These proceedings of the first Quantum Probability meeting held in Oberwolfach is the fourth in a series begun with the 1982 meeting of Mondragone and continued in Heidelberg ('84) and in Leuven ('85). The main topics discussed were: quantum stochastic calculus, mathematical models of quantum noise and their applications to quantum optics, the quantum Feynman-Kac formula, quantum probability and models of quantum statistical mechanics, the notion of conditioning in quantum probability and related problems (dilations, quantum Markov processes), quantum central limit theorems. With the exception of Kümmerer's review article on Quantum Markov Processes, all contributions are original research papers.

Proceedings of a Conference held in Oberwolfach, FRG, January 25-31, 1987

Quantum Probability and Applications III

The purpose of this volume is examine bio-informatics and quantum information, which are growing rapidly at present, and to attempt to connect the two, with a view to enumerating and solving the many fundamental problems they entail. To this end, we look for interdisciplinary bridges in mathematics, physics, and information and life sciences. In particular, research into a new paradigm for information science and life science on the basis of quantum theory is emphasized.

From Quantum Information to Bio-informatics : Tokyo University of Science, Japan, 14-17 March 2007

Quantum Bio-informatics

Franco Fagnola

The dynamics of infinite classical lattice systems has been considered and has led to the study of the properties of ergodicity and convergence to equilibrium of a new class of Markov semigroups. Quantum analogues of these semigroups have also been considered. However, the problem of deriving these Markovian semigroups and, what is much more interesting, the associated stochastic flows, as limits of Hamiltonian systems, rather than postulating their form on a phenomenological basis, is essentially open both in the classical case and in the quantum case. This book presents a conjecture that, by coupling a quantum spin system in finite volume to a quantum field via a suitable interaction, applying the stochastic golden rule and taking the thermodynamic limit, one may obtain a class of quantum flows which, when restricted to an appropriate Abelian subalgebra, gives rise to the classical interacting particle systems studied in classical statistical mechanics.

Lecture Notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000

Quantum Interacting Particle Systems

Takeyuki Hida

The topics discussed in this book can be classified into three parts: . (i) Gaussian processes. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed. (ii) White noise analysis. This book includes the notes of the series of lectures delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called OC generalized white noise functionalsOCO, and sometimes OC Hida distributionOCO. (iii) Variational calculus for random fields. This topic will certainly represent one of the driving research lines for probability theory in the next century, as can be seen from several papers in this volume. Sample Chapter(s). Chapter 1: Analysis of Brownian Functionals (1,502 KB). Contents: General Theory of White Noise Functionals; Gaussian and Other Processes; Infinite Dimensional Harmonic Analysis and Rotation Group; Quantum Theory; Feynman Integrals and Random Fields; Variational Calculus and Random Fields; Application to Biology. Readership: Graduate students and researchers in the fields of probability theory, functional analysis, statistics and theoretical physics."

Selected Papers of Takeyuki Hida

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 ?-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.

Quantum Probability & Related Topics

The purpose of this proceedings volume is to return to the starting point of bio-informatics and quantum information, fields that are growing rapidly at present, and to seriously attempt mutual interaction between the two, with a view to enumerating and solving the many fundamental problems they entail. For such a purpose, we look for interdisciplinary bridges in mathematics, physics, information and life sciences, in particular, research for new paradigm for information science and life science on the basis of quantum theory. Contents:The QP–DYN Algorithms (L Accardi et al.)New Types of Quantum Entropies and Additive Information Capacities (V P Belavkin)Self-Collapses of Quantum Systems and Brain Activities (K-H Fichtner et al.)The Passage from Digital to Analogue in White Noise Analysis and Applications (T Hida)On Quantum Algorithm for Exptime Problem (S Iriyama & M Ohya)On Sufficient Algebraic Conditions for Identification of Quantum States (A Jamiołkowski)Classical Wave Model of Quantum-Like Processing in Brain (A Khrennikov)Entanglement Mapping vs. Quantum Conditional Probability Operator (D Chruściński et al.)Space(-Time) Emergence as Symmetry Breaking Effect (I Ojima)On the Correspondence between Newtonian and Functional Mechanics (E V Piskovskiy & I V Volovich)Signaling Network of Environmental Sensing and Adaptation in Plants: Key Roles of Calcium Ion (K Kuchitsu & T Kurusu)NetzCope: A Tool for Displaying and Analyzing Complex Networks (M J Barber et al.)and other papers Readership: Researchers in quantum information, quantum physics, bio-informatics and life science. Keywords:Quantum Information;Quantum Probability;Quantum Computer;Bioinformatics;Genes;Adaptive Dynamics;White Noise Analysis;Entanglement;Quantum Entropy;SuperconductivityKey Features:Quantum informationBio-InformaticsGlobal research mixing the Quantum information and Bio-Informatics with various mathematical sciences

From Quantum Information to Bio-Informatics

Quantum Bio-Informatics IV

Michael Schurmann

This volume contains the latest results in the fields of quantum probability and infinite dimensional analysis. The contributions range from classical probability, 'pure' functional analysis and foundations of quantum mechanics to applications in mathematical physics, quantum information theory and modern mathematical finance. This diversity illustrates that research in quantum probability and infinite dimensional analysis is very active and strongly involved in modern mathematical developments and applications.

Quantum Probability And Infinite Dimensional Analysis - Proceedings Of The 26th Conference

Yun Gang Lu

Igor Volovich

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.

Luigi Accardi

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