  Quantum simulation is one of the core areas in the development of quantum
technologies. Among the various simulation platforms, integrated waveguides
have proven to be a powerful and versatile tool. One important aspect of
quantum simulation is the analysis of open quantum systems. In most practical
applications it is in fact essential to understand and control the dynamics
between the quantum system and its environment. Typical effects of interest for
example involve decoherence or memory effects, which lead to non-Markovian
behavior.
  In this work we establish integrated waveguides as a tool for the simulation
of open quantum systems. Using polarization as well as a photon's path degree
of freedom, we implement the coupling of a qubit with a low dimensional
discrete environment. Based on a measure of non-Markovianity, we define and
quantify specific types of information and information transfer between system
and environment. Experimentally we implement and verify non-Markovian evolution
in an optical waveguide array and analyze types of information flow between
system and environment realizable through integrated photonics.
