Wigner Function and Decoherence

I briefly review the role of the Wigner function in the study of the quantum-to-classical transition through interaction with the environment (decoherence). My contribution to the Fifth Wigner Symposium in Vienna touches upon two of Wigner’s fields of interest: His work on the interpretation of quantum theory [1] and his discussion of quasi-probability functions as encoded in the famous Wigner function [2]. As far as the interpretation is concerned, a crucial role in [1] is attributed to a result by Zeh [3] showing that it is usually very unrealistic to consider systems as being isolated from their natural environment. Except for small objects such as atoms and small molecules, they are quantum-entangled with a huge number of other degrees of freedom. This fact must therefore be taken into account to gain a proper interpretation of quantum theory. Under ordinary circumstances, these correlations with the environment lead to the local appearance of classical properties – a process known as decoherence (see the comprehensive review [4], where all necessary details can be found). Amongst the most important features of decoherence is its ubiquitous, unavoidable, occurrence as well as its irreversible nature. Technically, decoherence is investigated through the local, reduced, density matrix after the degrees of freedom of the environment are traced out. It is important to emphasise that the interaction with the environment leads to the emergence of a distinguished local “pointer basis” which is stable in time and which defines the local property that is called “classical”. The process of decoherence has been experimentally monitored in quantum optics experiments [5]. To appear in the Proceedings of the Fifth Wigner Symposium, edited by P. Kasperkovitz (World Scientific, Singapore, 1998).