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arXiv · 1205.3682

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

Jianxin Chen·Zhengfeng Ji·Mary Beth Ruskai·Bei Zeng·Duan-Lu Zhou
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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.

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Jianxin Chen, Zhengfeng Ji, Mary Beth Ruskai, Bei Zeng, Duan-Lu Zhou. 2012-05-16. Comment on some results of Erdahl and the convex structure of reduced density matrices. https://doi.org/10.1063/1.4736842

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