On properties of the space of quantum states and their application to the construction of entanglement monotones

Maxim E Shirokov
2010 Izvestiya: Mathematics  
We consider two properties of the set of quantum states as a convex topological space and some their implications concerning the notions of a convex hull and of a convex roof of a function defined on a subset of quantum states. By using these results we analyze two infinite-dimensional versions (discrete and continuous) of the convex roof construction of entanglement monotones, which is widely used in finite dimensions. It is shown that the discrete version may be 'false' in the sense that the
more » ... esulting functions may not possess the main property of entanglement monotones while the continuous version can be considered as a 'true' generalized convex roof construction. We give several examples of entanglement monotones produced by this construction. In particular, we consider an infinite-dimensional generalization of the notion of Entanglement of Formation and study its properties.
doi:10.1070/im2010v074n04abeh002510 fatcat:ejxg6nf2ejfjppqcvooayypkba