Frequently Asked Questions about Decoherence

We give a short, critical review of the issue of decoherence. We establish the most general framework in which decoherence can be discussed, how it can be quantified and how it can be measured. We focus on environment induced decoherence and its degree of usefulness for the interpretation of quantum theory. We finally discuss the emergence of a classical world. An overall emphasis is given in pointing at common fallacies and misconceptions. 1. What is meant by decoherence? In full generality, decoherence can be defined as the phenomenon by which quantum mechanical systems behave as though they are described by classical probability theory. In other words, a quantum mechanical system exhibits decoherence, when all typical features of quantum mechanical probability are suppressed. Since probability refers to the statistical properties of systems under study, decoherence refers to behaviour that can be inferred from the statistical analysis in a collection of identically prepared systems . Quantum theory is a theory of complex amplitudes, a fact that is responsible for the distinctive features of quantum probability. In particular It implies the existence of offdiagonal elements of the density matrix. Given a density matrix ρ̂, the state of a system is specified not only by the probability distribution with respect to a basis |i〉, pi = 〈i|ρ̂|i〉, but also by the off-diagonal elements 〈i|ρ̂|j〉. The latter have no analogue in classical probability. Interference phases appear when we study the probabilistic aspects of quantum systems at successive instants of time. This behaviour is highlighted by the two-slit experiment. Consider a system prepared at a state |ψ〉 and experimen1 Here, we shall not consider decoherence in theories that employ fundamental modifications of quantum theory, such as the addition of stochastic terms in Schrödinger’s equation [1]. Our focus is on classical behaviour and its emergence from the standard quantum mechanical formalism.