Quantum stochastic calculus

DOI10.1007/BF01095973zbMath0732.60066OpenAlexW2078065102MaRDI QIDQ808522

Alexandr S. Holevo

Publication date: 1991

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01095973

zbMATH Keywords

quantum stochastic calculussymmetric Fock spacechronologically ordered exponentsquantum Itô formula

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative dynamical systems (46L55) Stochastic processes (60G99) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Quantum stochastic calculus (81S25) Stochastic integrals (60H05)

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Fault tolerant quantum filtering and fault detection for quantum systems ⋮ Fault tolerant filtering and fault detection for quantum systems driven by fields in single photon states ⋮ Applications of Quantum Stochastic Processes in Quantum Optics ⋮ Quantum control and information processing ⋮ Quantum filtering for systems driven by fields in single photon states and superposition of coherent states using non-Markovian embeddings ⋮ A phase-space formulation and Gaussian approximation of the filtering equations for nonlinear quantum stochastic systems ⋮ Quantum linear coherent controller synthesis: a linear fractional representation approach ⋮ Direct coupling coherent quantum observers with discounted mean square performance criteria and penalized back-action ⋮ Multi-point Gaussian states, quadratic-exponential cost functionals, and large deviations estimates for linear quantum stochastic systems ⋮ Parametric randomization, complex symplectic factorizations, and quadratic-exponential functionals for Gaussian quantum states

Cites Work

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• Structure of Markov cocycles on Fock space
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• The essentially commutative dilations of dynamical semigroups on \(M_ n\)
• The Ito-Clifford integral
• On the generators of quantum dynamical semigroups
• Quantum mechanical Wiener processes
• Decomposable processes and continuous products of probability spaces
• Symmetric Hilbert spaces and related topics. Infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes
• Multiple Wiener integral
• Spectral Type of the Shift Transformation of Differential Processes With Stationary Increments
• On a Hilbert space of analytic functions and an associated integral transform part I
• Operator stochastic differential equations and stochastic semigroups
• Quelques applications de la formule de changement de variables pour les semimartingales

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