  Entanglement is a non local property of quantum states which has no classical
counterpart and plays a decisive role in quantum information theory. Several
protocols, like the teleportation, are based on quantum entangled states.
Moreover, any quantum algorithm which does not create entanglement can be
efficiently simulated on a classical computer. The exact role of the
entanglement is nevertheless not well understood. Since an exact analysis of
entanglement evolution induces an exponential slowdown, we consider
approximative analysis based on the framework of abstract interpretation. In
this paper, a concrete quantum semantics based on superoperators is associated
with a simple quantum programming language. The representation of entanglement,
i.e. the design of the abstract domain is a key issue. A representation of
entanglement as a partition of the memory is chosen. An abstract semantics is
introduced, and the soundness of the approximation is proven.
