> PRESENTATION:
Andrzej Jamiolkowski is professor of theoretical physics at the Nicolaus Copernicus University in Torun, Poland. He is expert of quantum mechanics of open system. Well known are his studies on positivity of maps. He graduated in physics from the University of Warsaw in 1969 and from the Nicolaus Copernicus University in Torun obtained in 1973 his Ph.D. in theoretical physics and in 1983 postdoctoral degree. He was a vice-rector of the Nicolaus Copernicus University in the years 1986-1999 and then the rector in the years 1993-1999. He attended the long-term foreign scholarships in Munich, Oldenburg and Marburg and participated in numerous studio journeys e.g. to American universities, at the USA government's s invitation, and to European universities (e.g. Kings College in London). He lectured and carried out research out of the country over 4 years. Since 1 January 2000 till end of 2001 he was a vice-chairman of the Main Board of Higher Education and since 1 January 2002 till now he is the President of the Polish State Committee for Accreditation.

The question of the minimal number r of observables Q1 , …, Qr , whose mean values at some instants t1 , …, ts determine the statistical state of a d-level open quantum system is discussed. We assume that the time evolution of the system in question is given by a semigroup of linear transformations with a generator L. A similar problem of the minimal number p of moments of observations, which are necessary for reconstruction of trajectories is also addressed. To give an exact answer to the above questions we introduce two notions: index of cyclicity and index of reconstructibility of the system.