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q-White noise and non-adapted stochastic integral

100%

Ji U., Min B.

Banach Center Publications

2006

tom 73

nr 1

267-275

The q-white noise is studied as the time derivative of the q-Brownian motion. As an application of the q-white noise, a non-adapted (non-commutative) stochastic integral with respect to the q-Brownian motion is constructed.

Quantum Itô algebra and quantum martingale

100%

Belavkin V., Ji U.

Banach Center Publications

2007

tom 78

nr 1

47-58

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.

Ograniczanie wyników

2 Banach Center Publications

2 Ji U.

1 Belavkin V.

1 Min B.

1 2007

1 2006

Wyniki wyszukiwania

q-White noise and non-adapted stochastic integral

Quantum Itô algebra and quantum martingale