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Entanglement is a non local property of quantum states which has no classicalcounterpart and plays a decisive role in quantum information theory. Severalprotocols, like the teleportation, are based on quantum entangled states.Moreover, any quantum algorithm which does not create entanglement can beefficiently simulated on a classical computer. The exact role of theentanglement is nevertheless not well understood. Since an exact analysis ofentanglement evolution induces an exponential slowdown, we considerapproximative analysis based on the framework of abstract interpretation. Inthis paper, a concrete quantum semantics based on superoperators is associatedwith a simple quantum programming language. The representation of entanglement,i.e. the design of the abstract domain is a key issue. A representation ofentanglement as a partition of the memory is chosen. An abstract semantics isintroduced, and the soundness of the approximation is proven.

Quantum entanglement analysis based on abstract interpretation