PIRSA:08090062

Bipartite states of low rank are almost surely entangled

Ruskai, M.B. (2008). Bipartite states of low rank are almost surely entangled. Perimeter Institute. https://pirsa.org/08090062

Ruskai, Mary Beth. Bipartite states of low rank are almost surely entangled. Perimeter Institute, Sep. 22, 2008, https://pirsa.org/08090062 

          @misc{ pirsa_PIRSA:08090062,
            doi = {10.48660/08090062},
            url = {https://pirsa.org/08090062},
            author = {Ruskai, Mary Beth},
            keywords = {Quantum Information},
            language = {en},
            title = {Bipartite states of low rank are almost surely entangled},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {sep},
            note = {PIRSA:08090062 see, \url{https://pirsa.org}}
          }

Mary Beth Ruskai

University of Massachusetts Lowell

Talk number
PIRSA:08090062
Collection
Talk Type
Subject
Abstract
There are many results showing that the probability of entanglement is high for large dimensions. Recently, Arveson showed that the probability of entanglement is zero when the rank of a bipartite state is no larger than half the dimension of the smaller space. We show that that the probability of entanglement is zero when the rank of a bipartite state is no larger than half the maximum of the rank of its two reduced density matrices. Our approach is quite different from that of Arveson and uses a different measure. But both approaches show that the separable states lie in a lower dimensional manifold given a reasonable parameterization of the separable states. This is joint work with Elisabeth Werner, using on characterizations of the extreme points of qubit channels given by Ruskai, Szarek and Werner and the extreme points of entanglement breaking channels given by M. Horodecki, Shor and Ruskai.