# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Controlled quantum open systems. (English) Zbl 1069.81547
Benatti, Fabio (ed.) et al., Irreversible quantum dynamics. Papers of the conference on ‘Irreversible quantum dynamics’, Trieste, Italy, July 29 – August 2, 2002. Berlin: Springer (ISBN 3-540-40223-3/hbk). Lect. Notes Phys. 622, 121-139 (2003).
Summary: The theory of controlled quantum open systems describes quantum systems interacting with quantum environments and influenced by external forces varying according to given algorithms. It is aimed, for instance, to model quantum devices which can find applications in the future technology based on quantum information processing. One of the main problems making difficult the practical implementations of quantum information theory is the fragility of quantum states under external perturbations. The aim of this note is to present the relevant results concerning ergodic properties of open quantum systems which are useful for the optimization of quantum devices and noise (errors) reduction. In particular we present mathematical characterization of the so-called “decoherence-free subspaces” for discrete and continuous-time quantum dynamical semigroups in terms of ${C}^{*}$-algehras and group representations. We analyze the non-Markovian models also, presenting the formulas for errors in the Born approximation. The obtained results are used to discuss the proposed different strategies of error reduction.

##### MSC:
 81S25 Quantum stochastic calculus 81Q05 Closed and approximate solutions to quantum-mechanical equations