%0 Journal Article
%J Journal of Mathematical Physics
%D 2012
%T Comment on some results of Erdahl and the convex structure of reduced density matrices
%A Jianxin Chen
%A Zhengfeng Ji
%A Mary Beth Ruskai
%A Bei Zeng
%A Duan-Lu Zhou
%X In J. Math. Phys. 13, 1608-1621 (1972), Erdahl considered the convex structure of the set of $N$-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the $m$-body setting and to the more general quantum marginal problem. We describe these extensions, but can not resolve a problem in the proof of Erdahl's claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when $2m \geq N$ every extreme point of the set of $N$-representable $m$-body reduced density matrices has a unique pre-image in both the symmetric and anti-symmetric setting. Moreover, this extends to the quantum marginal setting for a pair of complementary $m$-body and $(N-m)$-body reduced density matrices.
%B Journal of Mathematical Physics
%V 53
%P 072203
%8 2012/05/16
%G eng
%U http://arxiv.org/abs/1205.3682v1
%N 7
%! J. Math. Phys.
%R 10.1063/1.4736842