Quantum Itô algebra and quantum martingale
Volume 78 / 2007
Banach Center Publications 78 (2007), 47-58
MSC: Primary 81S25; Secondary 46F25.
DOI: 10.4064/bc78-0-3
Abstract
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 $\star$-algebra parameterizing the quantum Itô algebra.
