We study the stabilities of quantum states of macroscopic systems, against
noises, against perturbations from environments, and against local
measurements. We show that the stabilities are closely related to the cluster
property, which describes the strength of spatial correlations of fluctuations
of local observables, and to fluctuations of additive operators. The present
theory has many applications, among which we discuss the mechanism of phase
transitions in finite systems and quantum computers with a huge number of
qubits.Comment: Proceedings of the Japan-Italy Joint Waseda Workshop on "Fundamental
Problems in Quantum Mechanics", 27-29 September, 2001, Tokyo, Japan. (Edited
by S. Tasaki, to be published from World Scientific, 2002) 7 pages, no
figure