Quantum Itô algebra and quantum martingale

• Autorzy: Viacheslav Belavkin , Un Cig Ji
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study a representation of the quantum Itô algebra in Fock space and then by using a noncommutative Radon-Nikodym type theorem we study the density operators of output states as quantum martingales, where the output states are absolutely continuous with respect to an input (vacuum) state. Then by applying quantum martingale representation we prove that the density operators of regular, absolutely continuous output states belong to the commutant of the ⋆-algebra parameterizing the quantum Itô algebra.

Kategorie tematyczne

• 81S25: Quantum stochastic calculus
• 46F25: Distributions on infinite-dimensional spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 78
• Numer: 1
• Strony: 47-58

Daty

wydano

2007

Twórcy

autor

Viacheslav Belavkin

• Mathematics Department, University of Nottingham, University Park, Nottingham NG7 2RD, UK

autor

Un Cig Ji

• Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763, Korea

Identyfikatory

DOI

10.4064/bc78-0-3