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arXiv · 1705.00097

A lambda calculus for density matrices with classical and probabilistic controls

Alejandro Díaz-Caro
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Abstract

In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, $λ_ρ$, 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, $λ_ρ^\circ$, take 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.

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Alejandro Díaz-Caro. 2017-11-20. A lambda calculus for density matrices with classical and probabilistic controls. https://doi.org/10.1007/978-3-319-71237-6_22

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