Typing Quantum Superpositions and Measurement

  • Alejandro Díaz-CaroEmail author
  • Gilles Dowek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10687)


We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis.


Quantum computing Lambda-calculus Algebraic linearity Linear logic Measurement 



We would like to thank Eduardo Bonelli, Luca Paolini, Simona Ronchi della Rocca and Luca Roversi for interesting comments and suggestions.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Universidad Nacional de Quilmes and CONICETBernalArgentina
  2. 2.Inria, LSV, ENS Paris-SaclayCachan CedexFrance

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