title: Stability of quantum states of finite macroscopic systems against classical noises, perturbations from environments, and local measurements.
abstract: We study the stability of quantum states of macroscopic systems of finite volume V. By using both the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is O(V) or less for a pure state, then it is not fragile for any weak classical noises or weak perturbations from environments. (ii) If square fluctuation of some additive operator is O(V2) for a pure state, then it is fragile for some of these. (iii) If a state, pure or mixed, has the "cluster property," then it is stable against local measurements, and vice versa. Among many applications, we discuss the mechanism of symmetry-breaking in finite systems.
authors.affiliation: Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8902, Japan. shmz@ASone.c.u-tokyo.ac.jp
authors.forename: Akira
authors.initials: A
authors.lastname: Shimizu
authors.forename: Takayuki
authors.initials: T
authors.lastname: Miyadera