IJPAM: Volume 49, No. 3 (2008)

MULTIPARAMETER QUANTUM PROCESSES
OVER THE CLIFFORD SHEET

William Joseph Spring
Quantum Information and Probability Group
School of Computer Science
University of Hertfordshire
Hatfield, Herts, AL10 9AB, U.K.
e-mail: j.spring@herts.ac.uk


Abstract.Quantum analogues of classical stochastic constructions have been developed in which a quantum stochastic base consists of a Hilbert space $\mathcal{H}$, a von Neumann algebra $\mathcal{A}$, a filtration $\{\mathcal{A}_z\}$, a gauge $m$ and a parameter space $I$. In this discussion we employ such a base to introduce multiparameter Clifford processes, quantum stochastic integrals, their relationships and properties.

Received: August 14, 2008

AMS Subject Classification: 15A66

Key Words and Phrases: quantum stochastic integral, isometry, martingale

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 3