White Noise Analysis and Quantum Information

Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore: Volume 34

This volume is to pique the interest of many researchers in the fields of infinite dimensional analysis and quantum probability. These fields have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. These fields are rather wide and are of a strongly interdisciplinary nature. For such a purpose, we strove to bridge among these interdisciplinary fields in our Workshop on IDAQP and their Applications that was held at the Institute for Mathematical Sciences, National University of Singapore from 3–7 March 2014. Readers will find that this volume contains all the exciting contributions by well-known researchers in search of new directions in these fields.

Sample Chapter(s)
Foreword (124 KB)
Extensions of Quantum Theory Canonically Associated to Classical Probability Measures (433 KB)

• Extensions of Quantum Theory Canonically Associated to Classical Probability Measures (Luigi Accardi)
• Hida Distribution Construction of Indefinite Metric (ϕ^p)_d (d ≥ 4) Quantum Field Theory (Sergio Albeverio and Minoru W Yoshida)
• A Mathematical Realization of von Neumann's Measurement Scheme (Masanari Asano, Masanori Ohya and Yuta Yamamori)
• On Random White Noise Processes with Memory for Time Series Analysis (Christopher C Bernido and M Victoria Carpio-Bernido)
• Self-Repelling (Fractional) Brownian Motion: Results and Open Questions (Jinky Bornales and Ludwig Streit)
• Normal Approximation for White Noise Functionals by Stein's Method and Hida Calculus (Louis H Y Chen, Yuh-Jia Lee and Hsin-Hung Shih)
• Sensitive Homology Searching Based on MTRAP Alignment (Toshihide Hara and Masanori Ohya)
• Some of the Future Directions of White Noise Theory (Takeyuki Hida)
• Local Statistics for Random Selfadjoint Operators (Peter D Hislop and Maddaly Krishna)
• Multiple Markov Properties of Gaussian Processes and Their Control (Win Win Htay)
• Quantum Stochastic Differential Equations Associated with Square of Annihilation and Creation Processes (Un Cig Ji and Kalyan B Sinha)
• Itô Formula for Generalized Real and Complex White Noise Functionals (Yuh-Jia Lee)
• Quasi Quantum Quadratic Operators of 𝕄₂(ℂ) (Farrukh Mukhamedov)
• New Noise Depending on the Space Parameter and the Concept of Multiplicity (Si Si)
• A Hysteresis Effect on Optical Illusion and Non-Kolmogorovian Probability Theory (Masanari Asano, Andrei Khrennikov, Masanori Ohya and Yoshiharu Tanaka)
• Note on Entropy-Type Complexity of Communication Processes (Noboru Watanabe)