Some Aspects of Quantum Correlations for Non-independent System

We study the preparation of states for non-independence systems, especially for CAR systems. There exists the restriction to construct a separable state on the total system from some states on subsystems. We show some distinct features of quantum correlations such as violation of triangle inequality of entropy and violation of LOCC. Those aspects are due to the non-independence of systems and never occur in any algebraic independent system, e.g. tensor product system. We introduce a new notion half-sided entanglement from our observation.

This is a joint work with Huzihiro Araki in part.