Abstract:

We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices, and furthermore we show that the associated operator system is unique and has a certain homogeneity property. Conversely, we show that the cone of completely positive maps on any operator system with that homogeneity property is a mapping cone. We also consider several related problems, such as characterizing cones that are closed under composition on the right by completely positive maps, and cones that are also semigroups, in terms of operator systems.

Authors:

• Nathaniel Johnston
• Erling Størmer

Download:

• Official publicationfrom Bulletin of the London Mathematical Society
• Preprint from arXiv:1102.2012 [math.OA]
• Local preprint [pdf]

• CP-Invariance and Complete Positivity in Quantum Information Theory – PDF, TeX
• Right CP-Invariant Cones of Superoperators – PDF, TeX

Cite as:

• N. Johnston and E. Størmer. Mapping Cones are Operator Systems. Bulletin of the London Mathematical Society, 2012. doi: 10.1112/blms/bds006

Related Papers:

• Partially Entanglement Breaking Maps and Right CP-Invariant Cones – an unpublished preprint that contains some results about right CP-invariant cones, which play a role in this paper