Europhys. Lett., 62 (6) , pp. 782-788 (2003)
Phases of quantum states in completely positive non-unitary evolutionJ. G. Peixoto de Faria1, A. F. R. de Toledo Piza1 and M. C. Nemes2
1 Departamento de Física-Matemática, Instituto de Física Universidade de São Paulo - C.P. 66318 05315-970 São Paulo, São Paulo, Brazil
2 Departamento de Física, Instituto de Ciências Exatas Universidade Federal de Minas Gerais - C.P. 702 30161-970 Belo Horizonte, Minas Gerais, Brazil
(Received 30 October 2002; accepted in final form 25 April 2003)
We define an operational notion of phases in interferometry for a quantum system undergoing a completely positive non-unitary evolution. This definition is based on the concepts of quantum measurement theory. The suitable generalization of the Pancharatnan connection allows us to determine the dynamical and geometrical parts of the total phase between two states linked by a completely positive map. These results reduce to the known expressions of the total, dynamical and geometrical phases for pure and mixed states evolving unitarily.
03.65.Vf - Phases: geometric; dynamic or topological.
03.65.Ta - Foundations of quantum mechanics; measurement theory.
03.65.Yz - Decoherence; open systems; quantum statistical methods.
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