Displaying similar documents to “Quantum stopping times and quasi-left continuity”

Markov chains approximation of jump–diffusion stochastic master equations

Clément Pellegrini (2010)

Annales de l'I.H.P. Probabilités et statistiques

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are solutions of stochastic differential equations obtained when describing the random phenomena associated to quantum continuous measurement of open quantum system. These equations, also called or , are usually of two different types: diffusive and of Poisson-type. In this article, we consider more advanced models in which jump–diffusion equations appear. These equations are obtained as a continuous time limit of martingale problems associated to classical Markov chains...

Quantum Itô algebra and quantum martingale

Viacheslav Belavkin, Un Cig Ji (2007)

Banach Center Publications

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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...

Quantum stochastic calculus on full Fock space

Michael Skeide (1998)

Banach Center Publications

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We present a new version of integration of time-adapted processes with respect to creation, annihilation and conservation processes on the full Fock space. Among the new features, in the first place, there is a new formulation of adaptedness which is both simpler and more general than the known ones. The new adaptedness allows for processes which are not restricted to be elements of some norm closure of the ∗-algebra which is generated by the basic creation processes.

Natural quantum operational semantics with predicates

Marek Sawerwain, Roman Gielerak (2008)

International Journal of Applied Mathematics and Computer Science

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A general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight...