A Lambda Calculus for Density Matrices with Classical and Probabilistic Controls

  • Alejandro Díaz-Caro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10695)


In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, \(\lambda _\rho \), follows the approach of classical control/quantum data, where the quantum data is represented by density matrices. We provide an interpretation for programs as density matrices and functions upon them. The second one, \(\lambda _\rho ^\circ \), takes advantage of the density matrices presentation in order to follow the mixed trace of programs in a kind of generalised density matrix. Such a control can be seen as a weaker form of the quantum control and data approach.


Lambda calculus Quantum computing Density matrices Classical control 



We want to thank the anonymous reviewer for some important references and suggestions on future lines of work.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Universidad Nacional de Quilmes & CONICETBuenos AiresArgentina

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