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Abstract
This paper considers Wigner functions and measures for infinitedimensional open quantum systems; important examples of such systems are objects of
quantum control theory. An axiomatic definition of coherent quantum feedback is proposed. A representation of the states of quantum systems in terms of Wigner measures is possible for systems having classical analogues; it is similar to the representation of the states of classical Hamiltonian systems in
terms of probability measures on the phase space. In both cases, the passage to a description of the state of a subsystem of some larger quantum system is implemented by means of the projection operation, because the phase space of the classical analogue of the ambient quantum system, being the union of some subsystems, is the Cartesian product of the phase spaces of the classical analogues of these subsystems.
quantum control theory. An axiomatic definition of coherent quantum feedback is proposed. A representation of the states of quantum systems in terms of Wigner measures is possible for systems having classical analogues; it is similar to the representation of the states of classical Hamiltonian systems in
terms of probability measures on the phase space. In both cases, the passage to a description of the state of a subsystem of some larger quantum system is implemented by means of the projection operation, because the phase space of the classical analogue of the ambient quantum system, being the union of some subsystems, is the Cartesian product of the phase spaces of the classical analogues of these subsystems.
Original language  English 

Pages (fromto)  99103 
Number of pages  5 
Journal  Doklady Mathematics 
Volume  91 
Issue number  2 
DOIs  
Publication status  Published  01 Mar 2015 
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 1 Finished

Quantum Stochastic Analysis for Nanophotonic Circuit Design
Engineering and Physical Sciences Research Council
01 Aug 2013 → 31 Mar 2015
Project: Externally funded research