@article{DiazCaro2019a,
  title         = {Two linearities for quantum computing in the lambda calculus},
  author        = {D{\'i}az-Caro, Alejandro and Dowek, Gilles and Rinaldi, Juan Pablo},
  year          = {2019},
  month         = dec,
  journal       = {Biosystems},
  volume        = {186},
  eid           = {104012},
  pages         = {104012},
  doi           = {10.1016/j.biosystems.2019.104012},
  archiveprefix = {arXiv},
  eprint        = {1601.04294},
  abstract      = {We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. 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.},
  keywords      = {quantum computing, lambda calculus, algebraic linearity, linear logic, measurement},
  note          = {Selected papers from the International Conference on the Theory and Practice of Natural Computing (TPNC) 2017},
  webnote       = {Selected papers from the International Conference on the Theory and Practice of Natural Computing (TPNC) 2017},
  bibsource     = qplbib
}

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