POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Quantum computation and quantum information
Quantum computation and quantum information
Classical deterministic complexity of Edmonds' Problem and quantum entanglement
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Towards a quantum programming language
Mathematical Structures in Computer Science
Quantum programming languages: survey and bibliography
Mathematical Structures in Computer Science
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Reasoning about Entanglement and Separability in Quantum Higher-Order Functions
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
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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.