Pure and mixed states

J. C. A. Barata, M. Brum, V. Chabu, R. Correa da Silva

Published 2019-09-13Version 1

In this article, we present an extensive review on the notion of pure states and mixtures as mathematical concepts that apply to both classical and quantum physical theories, as well as to any other theory depending on statistical description. Here, states will be presented as linear functionals on $C^*$ algebras, in a manner intended for the non-specialist reader; accordingly, basic literature on the subject will be provided. Finally, illustrative examples will be exposed together with a discussion on their meanings and implications. An example will be shown where a pure quantum state converges to a classical mixture of particles as the Planck's constant tends to zero.