An Introduction to Quantum Probability

Enrico G. Beltrametti, Gianni Cassinelli, Peter Carruthers

Luigi Accardi

Jerome R. Busemeyer

Emmanuel E. Haven, Andrei Yu. Khrennikov, Chenghu Ma +1 more

Luc Bouten, Ramon van Handel, M. R. James

This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum Itô calculus and its use in the modeling of physical systems. We use both reference probability and innovations methods to obtain quantum filtering equations for system-probe models from quantum optics.

Kai Lai Chung, Jean-Claude Zambrini

Introduction to Random Time: Prologue Stopping Martingale Stopped Random Past and Future Other Times From First to Last Gapless Time Markov Chain in Continuum Time The Trouble with Infinite Introduction to Quantum Randomness: Classical Prologue Standard Quantum Mechanics Probabilities in Standard Quantum Mechanics Feynman's Approach to Quantum Probabilities Schrodinger's Euclidean Quantum Mechanics Beyond Feynman's Approach Time for a Dialogue.