  We consider finite macroscopic systems, i.e., systems of large but finite
degrees of freedom, which we believe are poorly understood as compared with
small systems and infinite systems. We focus on pure states that do not have
the `cluster property.' Such a pure state is entangled macroscopically, and is
quite anomalous in view of many-body physics because it does not approach any
pure state in the infinite-size limit. However, we often encounter such
anomalous states when studying finite macroscopic systems, such as quantum
computers with many qubits and finite systems that will exhibit symmetry
breaking in the infinite-size limit. We study stabilities of such anomalous
states in general systems. In contrast to the previous works, we obtain general
and universal results, by making full use of the locality of the theory. Using
the general results, we discuss roles of anomalous states in quantum computers,
and the mechanism of emergence of a classical world from quantum theory.
