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WORLD SCIENTIFIC eBooks

Quantum probability communications : QP-PQ

R. L. Hudson, J. Martin Lindsay, Philippe Biane, Stéphane Attal

Published Jan 1, 1998• 1 citation
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Abstract

Extensions of Quantum Stochastic Calculus (S Attal) Quantum Ito Algebras: Axioms, Representations, Decompositions (V Belavkin) Free Probability for Probabilists (P Biane) Conditional Expectations on von Neumann Algebras (C Cecchini) Classical Probability Theory: An Outline of Stochastic Integrals and Diffusions (M Emery) Quantum Stochastic Differential Equations (F Fagnola) Canonical Commutation and Anticommutation Relations (M Fannes) Quantum and Classical Stochastic Calculus (A Holevo) An Introduction to Quantum Stochastic Calculus and Some of Its Applications (R Hudson) Stationary Processes in Quantum Probability (B Kummerer)

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Quantum probability and infinite dimensional analysis : from foundations to applications : Krupp-Kolleg Greifswald, Germany, 22-28 June, 2003

Michael Schürmann, Uwe Franz

Probability Measures in Terms of Creation, Annihilation and Neutral Operators (L Accardi et al.) Generating Function Methods for Orthogonal Polynomials and Jacobi-Szego Parameters (N Asai et al.) Multiquantum Markov Semigroups, Interacting Branching Processes and Nonlinear Kinetic Equations. Finite Dimensional Case (V Belavkin & C Williams) A Note on Vacuum-Adapted Semimartingales and Monotone Independence (A Belton) Regular Quantum Stochastic Cocycles have Exponential Product Systems (B V R Bhat & M Lindsay) Quantum Mechanics on the Circle Through Hopf q-Deformations of the Kinematical Algebra with Possible Applications to Levy Processes (V K Dobrev et al.) On Algebraic and Quantum Random Walks (D Ellinas) Dual Representations for the Schrodinger Algebra (P H Feinsilver & R Schott) A Limit Theorem for Conditionally Independent Beam Splittings (K H Fichtner et al.) On Quantum Logical Gates on a General Fock Space (W Feudenberg et al.) On an Argument of David Deutsch (R Gill) The Method of Double Product Integrals in Quantization of Lie Bialgebras (R Hudson) Asymptotics of Large Truncated Haar Unitary Matrices (J Reffy) Three Ways to Representations of Ba(E) (M Skeide) On Topological Entropy of Quotients and Extensions (J Zacharias) and other papers.

WORLD SCIENTIFIC eBooks•Jan 1, 2005•1 citation

Quantum Probability and Applications III: Proceedings of a Conference Held in Oberwolfach, Frg, January 25-31, 1987

Luigi Accardi, Wilhelm von Waldenfels

A note on Meyer's note.- Stochastic integration.- Quantum stochastic parallel transport on non-commutative vector bundles.- Input and output channels in quantum systems and quantum stochastic differential equations.- Some noncommutative Radon-Nikodym Theorems for von Neumann algebras.- Multidimensional quantum diffusions.- An application of de finetti's theorem.- The quantum Langevin equation from the independent-oscillator model.- Quantum poisson processes: Physical motivations and applications.- A noncommutative generalization of conditionally positive definite functions.- Contraction semigroups in L2 over a von neumann algebra.- Survey on a theory of non-commutative stationary markov processes.- Dynamical entropy for quantum systems.- An integral kernel approach to noise.- A note on shifts and cocycles.- Local measures in fock space stochastic calculus and a generalized ito-tanaka formula.- Representation of a class of quantum martingales II.- Conditional expectation in quantum probability.- Mutual quadratic variation and ito's table in quantum stochastic calculus.- On mixing properties of automorphisms of von neumann algebras related to measure space transformations.- First exit time: A theory of stopping times in quantum processes.- A central limit theorem on the free lie group.- Entropy, observability and the generalised second law of thermodynamics.- Remarks on asymptotic properties of groups of the bogoliubov transformations of car c*-algebras.- Linear and non-linear stochastic processes.- Detailed balance and critical slowing down.- Quantum martingales and stochastic integrals.

•May 1, 1988•1 citation

AN INTRODUCTION TO QUANTUM STOCHASTIC CALCULUS AND SOME OF ITS APPLICATIONS

R. L. Hudson

WORLD SCIENTIFIC eBooks•Feb 11, 2010•9 citations

An Introduction to Quantum Stochastic Calculus

Kalyanapuram Rangachari Parthasarathy

Springer eBooks•Jan 1, 1992•928 citations

Measurement and Filtering of Quantum Diffusion II

V. P. Belavkin

Next article Measurement and Filtering of Quantum Diffusion IIV. P. BelavkinV. P. Belavkinhttps://doi.org/10.1137/1139026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. N. Kolmogorov, Foundations of the Theory of Probability, Chelsea Publishing Company, New York, 1984 Google Scholar[2] John von Neumann, Mathematical foundations of quantum mechanics, Princeton University Press, Princeton, 1955xii+445, N.Y. 16,654a Google Scholar[3] A. S. Holevo, Probability and Stochastic Aspects of Quantum Theory, Princeton University Press, Princeton, N.J., 1955 Google Scholar[4] B. Misra and , E. C. G. Sudarshan, The Zeno's paradox in quantum theory, J. Mathematical Phys., 18 (1977), 756–763 10.1063/1.523304 55:5076 CrossrefGoogle Scholar[5] V. P. Belavkin, A stochastic calculus of quantum input-output processes and quantum nondemolition filteringCurrent problems in mathematics. Newest results, Vol. 36 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, 29–67, 187 91f:81074 Google Scholar[6] Viacheslav P. Belavkin, Nondemolition measurements, nonlinear filtering and dynamic programming of quantum stochastic processesModeling and control of systems in engineering, quantum mechanics, economics and biosciences (Sophia-Antipolis, 1988), Lecture Notes in Control and Inform. Sci., Vol. 121, Springer, Berlin, 1989, 245–265 1 231 124 0683.93084 CrossrefGoogle Scholar[7] V. P. Belavkin, Optimal quantum filtering of Markov signals, Problemy upravleniya i teoriya inform., 7 (1978), 345–360, (In Russian.) 0397.94001 Google Scholar[8] V. P. Belavkin, A. Blaquiere, Nondemolition measurement and control in quantum dynamical systemsInformation complexity and control in quantum physics (Udine, 1985), CISM Courses and Lectures, Vol. 294, Springer, Vienna, 1987, 311–329 913 955 CrossrefGoogle Scholar[9] V. P. Belavkin, B. Grigelionis, Stochastic posterior equations for quantum nonlinear filteringProbability theory and mathematical statistics, Vol. I (Vilnius, 1989), “Mokslas”, Vilnius, 1990, 91–109, Proceedings of the Fifth Vilnius Conference 93b:81126 0914.60082 Google Scholar[10] V. P. Belavkin, A quantum nonadapted stochastic calculus and nonstationary evolution in Fock scaleQuantum probability & related topics, QP-PQ, VI, World Sci. Publishing, River Edge, NJ, 1991, 137–179 92m:81119 0937.60045 CrossrefGoogle Scholar[11] Viacheslav P. Belavkin, Quantum stochastic calculus and quantum nonlinear filtering, J. Multivariate Anal., 42 (1992), 171–201 10.1016/0047-259X(92)90042-E 93m:81013 0762.60059 CrossrefGoogle Scholar[12] R. L. Hudson and , K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys., 93 (1984), 301–323 86e:46057 0546.60058 CrossrefGoogle Scholar[13] A. S. Holevo, Quantum stochastic calculus, Itogi nauki tekhniki. Modern problems of mathematics series. Newest achievements, 36 (1989), 3–28 Google Scholar[14] V. P. Belavkin, Quantum continual measurements and a posteriori collapse on CCR, Comm. Math. Phys., 146 (1992), 611–635 93j:81006 0757.60057 CrossrefGoogle Scholar[15] V. P. Belavkin, A posterior Schrödinger equation for continuous nondemolition measurement, J. Math. Phys., 31 (1990), 2930–2934 10.1063/1.528946 91m:81020 0718.47035 CrossrefGoogle Scholar[16] V. P. Belavkin and , P. Staszewski, Nondemolition observation of a free quantum particle, Phys. Rev., Ser. A, 45 (1992), 1347–1356 10.1103/PhysRevA.45.1347 CrossrefGoogle Scholar[17] M. P. Evans and , R. L. Hudson, Multidimensional quantum diffusionsQuantum probability and applications, III (Oberwolfach, 1987), Lecture Notes in Math., Vol. 1303, Springer, Berlin, 1988, 69–88 91a:46065 0648.46056 CrossrefGoogle Scholar[18] R. S. Liptser and , A. N. Shiryayev, Statistics of random processes. I, Springer-Verlag, New York, 1977x+394, Berlin 57:14125 R. S. Liptser and , A. N. Shiryayev, Statistics of random processes. II, Springer-Verlag, New York, 1978x+339, Berlin 58:7827 CrossrefGoogle Scholar[19] R. L. Stratonovitch, Conditional Markov Processes and their Application to Optimal Control Theory, Moscow State University, Moscow, 1966 Google Scholar[20] V. P. Belavkin, Chaotic states and stochastic integration in quantum systems, Russian Math. Surveys, 47 (1992), 47–106, (In Russian.) CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails Open-system many-body dynamics through interferometric measurements and feedbackPhysical Review A, Vol. 94, No. 5 | 17 November 2016 Cross Ref Continuous Quantum Hypothesis TestingPhysical Review Letters, Vol. 108, No. 17 | 1 April 2012 Cross Ref Volume 39, Issue 3| 1995Theory of Probability & Its Applications History Submitted:08 October 1991Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1139026Article page range:pp. 363-378ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Theory of Probability and Its Applications•Jan 1, 1995•2 citations

Quantum probability & related topics : QP-PQ

Luigi Accardi, A. Frigerio

On the stochastic limit of quantum chromodynamics, L. Accardi et al flows and imprimitivity systems, L. Accardi and A. Mohari fermion stochastic flows on quantum algebras, D. Applebaum examples of unbounded generators leading to nonconservative minimal semigroups, R.B.V. Bhat and K.B. Sinha on the structure of quantum Markov processes, C. Cecchini diffusion processes in fock space, F. Fagnola on the isomorphism of Poisson space and symmetric fock space, V. Liebscher non-linear master equation and non-crossing cumulants, P. Neu and R. Speicher a general central limit theorem and invariance principle, R. Speicher and W. von Waldenfels.

WORLD SCIENTIFIC eBooks•Jan 1, 1991•0 citations
Extensions of Quantum Stochastic Calculus (S Attal) Quantum Ito Algebras: Axioms, Representations, Decompositions (V Belavkin) Free Probability for Probabilists (P Biane) Conditional Expectations on von Neumann Algebras (C Cecchini) Classical Probability Theory: An Outline of Stochastic Integrals and Diffusions (M Emery) Quantum Stochastic Differential Equations (F Fagnola) Canonical Commutation and Anticommutation Relations (M Fannes) Quantum and Classical Stochastic Calculus (A Holevo) An Introduction to Quantum Stochastic Calculus and Some of Its Applications (R Hudson) Stationary Processes in Quantum Probability (B Kummerer)
Probability Measures in Terms of Creation, Annihilation and Neutral Operators (L Accardi et al.) Generating Function Methods for Orthogonal Polynomials and Jacobi-Szego Parameters (N Asai et al.) Multiquantum Markov Semigroups, Interacting Branching Processes and Nonlinear Kinetic Equations. Finite Dimensional Case (V Belavkin & C Williams) A Note on Vacuum-Adapted Semimartingales and Monotone Independence (A Belton) Regular Quantum Stochastic Cocycles have Exponential Product Systems (B V R Bhat & M Lindsay) Quantum Mechanics on the Circle Through Hopf q-Deformations of the Kinematical Algebra with Possible Applications to Levy Processes (V K Dobrev et al.) On Algebraic and Quantum Random Walks (D Ellinas) Dual Representations for the Schrodinger Algebra (P H Feinsilver & R Schott) A Limit Theorem for Conditionally Independent Beam Splittings (K H Fichtner et al.) On Quantum Logical Gates on a General Fock Space (W Feudenberg et al.) On an Argument of David Deutsch (R Gill) The Method of Double Product Integrals in Quantization of Lie Bialgebras (R Hudson) Asymptotics of Large Truncated Haar Unitary Matrices (J Reffy) Three Ways to Representations of Ba(E) (M Skeide) On Topological Entropy of Quotients and Extensions (J Zacharias) and other papers.
A note on Meyer's note.- Stochastic integration.- Quantum stochastic parallel transport on non-commutative vector bundles.- Input and output channels in quantum systems and quantum stochastic differential equations.- Some noncommutative Radon-Nikodym Theorems for von Neumann algebras.- Multidimensional quantum diffusions.- An application of de finetti's theorem.- The quantum Langevin equation from the independent-oscillator model.- Quantum poisson processes: Physical motivations and applications.- A noncommutative generalization of conditionally positive definite functions.- Contraction semigroups in L2 over a von neumann algebra.- Survey on a theory of non-commutative stationary markov processes.- Dynamical entropy for quantum systems.- An integral kernel approach to noise.- A note on shifts and cocycles.- Local measures in fock space stochastic calculus and a generalized ito-tanaka formula.- Representation of a class of quantum martingales II.- Conditional expectation in quantum probability.- Mutual quadratic variation and ito's table in quantum stochastic calculus.- On mixing properties of automorphisms of von neumann algebras related to measure space transformations.- First exit time: A theory of stopping times in quantum processes.- A central limit theorem on the free lie group.- Entropy, observability and the generalised second law of thermodynamics.- Remarks on asymptotic properties of groups of the bogoliubov transformations of car c*-algebras.- Linear and non-linear stochastic processes.- Detailed balance and critical slowing down.- Quantum martingales and stochastic integrals.
Next article Measurement and Filtering of Quantum Diffusion IIV. P. BelavkinV. P. Belavkinhttps://doi.org/10.1137/1139026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. N. Kolmogorov, Foundations of the Theory of Probability, Chelsea Publishing Company, New York, 1984 Google Scholar[2] John von Neumann, Mathematical foundations of quantum mechanics, Princeton University Press, Princeton, 1955xii+445, N.Y. 16,654a Google Scholar[3] A. S. Holevo, Probability and Stochastic Aspects of Quantum Theory, Princeton University Press, Princeton, N.J., 1955 Google Scholar[4] B. Misra and , E. C. G. Sudarshan, The Zeno's paradox in quantum theory, J. Mathematical Phys., 18 (1977), 756–763 10.1063/1.523304 55:5076 CrossrefGoogle Scholar[5] V. P. Belavkin, A stochastic calculus of quantum input-output processes and quantum nondemolition filteringCurrent problems in mathematics. Newest results, Vol. 36 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, 29–67, 187 91f:81074 Google Scholar[6] Viacheslav P. Belavkin, Nondemolition measurements, nonlinear filtering and dynamic programming of quantum stochastic processesModeling and control of systems in engineering, quantum mechanics, economics and biosciences (Sophia-Antipolis, 1988), Lecture Notes in Control and Inform. Sci., Vol. 121, Springer, Berlin, 1989, 245–265 1 231 124 0683.93084 CrossrefGoogle Scholar[7] V. P. Belavkin, Optimal quantum filtering of Markov signals, Problemy upravleniya i teoriya inform., 7 (1978), 345–360, (In Russian.) 0397.94001 Google Scholar[8] V. P. Belavkin, A. Blaquiere, Nondemolition measurement and control in quantum dynamical systemsInformation complexity and control in quantum physics (Udine, 1985), CISM Courses and Lectures, Vol. 294, Springer, Vienna, 1987, 311–329 913 955 CrossrefGoogle Scholar[9] V. P. Belavkin, B. Grigelionis, Stochastic posterior equations for quantum nonlinear filteringProbability theory and mathematical statistics, Vol. I (Vilnius, 1989), “Mokslas”, Vilnius, 1990, 91–109, Proceedings of the Fifth Vilnius Conference 93b:81126 0914.60082 Google Scholar[10] V. P. Belavkin, A quantum nonadapted stochastic calculus and nonstationary evolution in Fock scaleQuantum probability & related topics, QP-PQ, VI, World Sci. Publishing, River Edge, NJ, 1991, 137–179 92m:81119 0937.60045 CrossrefGoogle Scholar[11] Viacheslav P. Belavkin, Quantum stochastic calculus and quantum nonlinear filtering, J. Multivariate Anal., 42 (1992), 171–201 10.1016/0047-259X(92)90042-E 93m:81013 0762.60059 CrossrefGoogle Scholar[12] R. L. Hudson and , K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys., 93 (1984), 301–323 86e:46057 0546.60058 CrossrefGoogle Scholar[13] A. S. Holevo, Quantum stochastic calculus, Itogi nauki tekhniki. Modern problems of mathematics series. Newest achievements, 36 (1989), 3–28 Google Scholar[14] V. P. Belavkin, Quantum continual measurements and a posteriori collapse on CCR, Comm. Math. Phys., 146 (1992), 611–635 93j:81006 0757.60057 CrossrefGoogle Scholar[15] V. P. Belavkin, A posterior Schrödinger equation for continuous nondemolition measurement, J. Math. Phys., 31 (1990), 2930–2934 10.1063/1.528946 91m:81020 0718.47035 CrossrefGoogle Scholar[16] V. P. Belavkin and , P. Staszewski, Nondemolition observation of a free quantum particle, Phys. Rev., Ser. A, 45 (1992), 1347–1356 10.1103/PhysRevA.45.1347 CrossrefGoogle Scholar[17] M. P. Evans and , R. L. Hudson, Multidimensional quantum diffusionsQuantum probability and applications, III (Oberwolfach, 1987), Lecture Notes in Math., Vol. 1303, Springer, Berlin, 1988, 69–88 91a:46065 0648.46056 CrossrefGoogle Scholar[18] R. S. Liptser and , A. N. Shiryayev, Statistics of random processes. I, Springer-Verlag, New York, 1977x+394, Berlin 57:14125 R. S. Liptser and , A. N. Shiryayev, Statistics of random processes. II, Springer-Verlag, New York, 1978x+339, Berlin 58:7827 CrossrefGoogle Scholar[19] R. L. Stratonovitch, Conditional Markov Processes and their Application to Optimal Control Theory, Moscow State University, Moscow, 1966 Google Scholar[20] V. P. Belavkin, Chaotic states and stochastic integration in quantum systems, Russian Math. Surveys, 47 (1992), 47–106, (In Russian.) CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails Open-system many-body dynamics through interferometric measurements and feedbackPhysical Review A, Vol. 94, No. 5 | 17 November 2016 Cross Ref Continuous Quantum Hypothesis TestingPhysical Review Letters, Vol. 108, No. 17 | 1 April 2012 Cross Ref Volume 39, Issue 3| 1995Theory of Probability & Its Applications History Submitted:08 October 1991Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1139026Article page range:pp. 363-378ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics
On the stochastic limit of quantum chromodynamics, L. Accardi et al flows and imprimitivity systems, L. Accardi and A. Mohari fermion stochastic flows on quantum algebras, D. Applebaum examples of unbounded generators leading to nonconservative minimal semigroups, R.B.V. Bhat and K.B. Sinha on the structure of quantum Markov processes, C. Cecchini diffusion processes in fock space, F. Fagnola on the isomorphism of Poisson space and symmetric fock space, V. Liebscher non-linear master equation and non-crossing cumulants, P. Neu and R. Speicher a general central limit theorem and invariance principle, R. Speicher and W. von Waldenfels.