Algorithmic approach to quantum theory 3: bipartite entanglement dynamics in systems with random unitary transformations

Abstract

We study the problem of the most economical representation of entangled states in the classical simulations. The idea is to reduce the general form of entanglement to the bipartite entanglement which has the short representation through Schmidt expansion. The problem of such reduction is stated exactly and discussed. The example is given which shows that if we allow the linear transformation (not only unitary), the general form of entanglement cannot be described in terms of bipartite entanglement. We also study the entanglement dynamics of 2 and 3 level atoms interacting randomly and find interesting dependence of the number of its excited levels.