Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 64, Issue 6, 2001, Pages 5-

  Štelmachovič, Peter ^a   Bužek, Vladimír ^a,b  

^a INSTITUTE OF PHYSICS   (Slovakia)

^b MASARYK UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84864427474     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.64.062106     Document Type: Article

References (10)

1. E. B. Davies, Quantum Theory of Open Systems (Academic, London, 1976).
2. J. Preskill, “Lecture notes for the course Information for Physics 219/Computer Science 219, Quantum Computation,” www.theory.caltech.edu/people/preskill/ph229.
3. K. Kraus, States, Effects and Operations (Springer-Verlag, Berlin, 1983).
4. L. D. Romero and J. P. Paz, Phys. Rev. A 55, 4070 (1997);
5. Phys. Rev. AV. Hakim and V. Ambegaokar, 32, 423 (1995);
6. P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994).
7. To be mathematically correct (Formula presented) are not generators of the corresponding group but (Formula presented) multiplied by the complex constant i. The complex constant is usually omitted and the (Formula presented) alone are called generators. The same remark holds for generators (Formula presented)
8. V. Bužek, Phys. Rev. A 58, 1723 (1998).
9. This inversion is possible due to the fact that in the finite-dimensional Hilbert spaces matrix elements of density operators are analytic functions. Consequently, (Formula presented) are nonsingular operators (except maybe for a set of isolated values of (Formula presented) in which case the inverse operators (Formula presented) do exist.
10. Here we emphasize that we can choose the factorized density operator. It does not mean that the correlated density operator cannot be used. For more discussion see the end of the previous paragraph.