TY - JOUR
T1 - Comment on some results of Erdahl and the convex structure of reduced density matrices
JF - Journal of Mathematical Physics
Y1 - 2012
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - Mary Beth Ruskai
A1 - Bei Zeng
A1 - Duan-Lu Zhou
AB - 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.
VL - 53
U4 - 072203
UR - http://arxiv.org/abs/1205.3682v1
CP - 7
J1 - J. Math. Phys.
U5 - 10.1063/1.4736842
ER -