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Q-adapted quantum stochastic integrals and differentials in Fock scale

100%

Belavkin V., Brown M.

Banach Center Publications

2011

tom 96

nr 1

51-66

In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field $𝔉_𝕏$, of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally, Q-adapted dynamics is discussed, including Bosonic (Q = I), Fermionic (Q = -I), and monotone (Q = O) quantum dynamics. These may be of particular interest to quantum field theory, quantum open systems, and quantum theory of stochastic processes.

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 Belavkin V.

1 Brown M.

1 Ji U.

1 2011

1 2007

Wyniki wyszukiwania

Q-adapted quantum stochastic integrals and differentials in Fock scale

Quantum Itô algebra and quantum martingale