



@article {1458,
	title = {Comment on some results of Erdahl and the convex structure of reduced  density matrices},
	journal = {Journal of Mathematical Physics},
	volume = {53},
	year = {2012},
	month = {2012/05/16},
	pages = {072203},
	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{\textquoteright}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.
},
	doi = {10.1063/1.4736842},
	url = {http://arxiv.org/abs/1205.3682v1},
	author = {Jianxin Chen and Zhengfeng Ji and Mary Beth Ruskai and Bei Zeng and Duan-Lu Zhou}
}
@article {1455,
	title = {Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians},
	year = {2010},
	month = {2010/10/13},
	abstract = {  The structure of the ground spaces of quantum systems consisting of local
interactions is of fundamental importance to different areas of physics. In
this Letter, we present a necessary and sufficient condition for a subspace to
be the ground space of a k-local Hamiltonian. Our analysis are motivated by the
concept of irreducible correlations studied by [Linden et al., PRL 89, 277906]
and [Zhou, PRL 101, 180505], which is in turn based on the principle of maximum
entropy. It establishes a better understanding of the ground spaces of local
Hamiltonians and builds an intimate link of ground spaces to the correlations
of quantum states.
},
	url = {http://arxiv.org/abs/1010.2739v4},
	author = {Jianxin Chen and Zhengfeng Ji and Mary Beth Ruskai and Bei Zeng and Duanlu Zhou}
}
