Comment on some results of Erdahl and the convex structure of reduced density matrices

TitleComment on some results of Erdahl and the convex structure of reduced density matrices
Publication TypeJournal Article
Year of Publication2012
AuthorsChen, J, Ji, Z, Ruskai, MBeth, Zeng, B, Zhou, D-L
JournalJournal of Mathematical Physics
Volume53
Issue7
Pages072203
Date Published2012/05/16
Abstract

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.

URLhttp://arxiv.org/abs/1205.3682v1
DOI10.1063/1.4736842
Short TitleJ. Math. Phys.