A lambda calculus for density matrices with classical and probabilistic controls
Abstract
In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, λ, 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, 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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