On quantum Itô algebras and their decompositions

DOI10.1023/A:1007477417830zbMath0909.46051arXivmath-ph/0512071OpenAlexW1580521100MaRDI QIDQ1267808

Vyacheslav P. Belavkin

Publication date: 8 April 1999

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0512071

zbMATH Keywords

stochastic calculusquantum noisethermal noiseaxiomatic characterizationLévy-Khinchin theoremnoncommutative Itô algebraorthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebrapseudo-Euclidean fundamental representationquantum Poisson noise

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Quantum stochastic calculus (81S25) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (8)

Noncommutative dynamics and generalized master equations ⋮ Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions ⋮ Lyapunov control of squeezed noise quantum trajectory ⋮ Quantum Lévy–Itô algebras and non-commutative stochastic analysis ⋮ Coherent quantum LQG control ⋮ The Unitarity Conditions for the Square of White Noise ⋮ Quantum feedback networks: Hamiltonian formulation ⋮ QUANTUM PROBABILITIES AND PARADOXES OF THE QUANTUM CENTURY

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