Measurements and confluence in quantum lambda calculi with explicit   qubits
  This paper demonstrates how to add a measurement operator to quantum lambda-calculi. A proof of the consistency of the semantics is given through a proof of confluence presented in a sufficiently general way to allow this technique to be used for other languages. The method described here may be applied to probabilistic rewrite systems in general, and to add measurement to more complex languages such as QML or Lineal, which is the subject of further research. 
Alejandro D\'iaz-Caro, Pablo Arrighi, Manuel Gadella and Jonathan   Grattage