Two-dimensional quantum Bernoulli process and the related central limit theorem

Abstract

In this paper, we introduce a quantum decomposition of a two-dimensional Bernoulli random variable [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text]. Based on this quantum decomposition, we defined the two-dimensional quantum Bernoulli process and set a corresponding central limit theorem, both in the sense of quantum moments and in the sense of characteristic function.