Environment-induced decoherence, classicality, and consistency of quantum histories

Abstract

We prove that for an open system, in the Markovian regime, it is always possible to construct an infinite number of nontrivial sets of histories that exactly satisfy the probability sum rules. In spite of being perfectly consistent, these sets manifest a very nonclassical behavior: they are quite unstable under the addition of an extra instant to the list of times defining the history. To eliminate this feature—the implications of which we discuss—and to achieve the stability that characterizes the quasiclassical domain, it is necessary to separate the instants which define the history by time intervals significantly larger than the typical decoherence time. In this case environment induced superselection is very effective. The quasiclassical domain is defined by predictably evolving perferred states, ‘‘pointer projectors,’’ which give rise to consistent preferred sets of histories.