کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
421639 | 684923 | 2015 | 17 صفحه PDF | دانلود رایگان |
We propose a new 'quantum domain theory' in which Scott-continuous functions are replaced by Scott-continuous natural transformations.Completely positive maps are widely accepted as a model of first-order quantum computation. We begin by establishing a categorical characterization of completely positive maps as natural families of positive maps. We explore this categorical characterization by building various representations of quantum computation based on different structures: affine maps between cones of positive elements, morphisms of algebras of effects, and affine maps of convex sets of states. By focusing on convex dcpos, we develop a quantum domain theory and show that it supports some important constructions such as tensor products by quantum data, and lifting.
Journal: Electronic Notes in Theoretical Computer Science - Volume 319, 21 December 2015, Pages 369-385