2 - Shannon’s Theorem in Quantum Data

Abstract

Another variant of Shannon’s theorem, known as the Shannon–McMillan theorem, was the subject of work carried out by Ogata. This chapter focuses mainly on the quantum aspects of data. The Shannon–McMillan theorem stipulates that an ergodic system has, as its solution, a set of typical series satisfying the asymptotic equipartition property. This theorem explains the meaning of entropy, which gives the dimension of the typical series. The asymptotic equipartition property can be seen as the equivalence of sets; it also makes it possible to give the potential compression rate in source coding theory.