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| comment on some results of erdahl and the convex structure of reduced density matrices | |
| Chen Jianxin; Ji Zhengfeng; Ruskai Mary Beth; Zeng Bei; Zhou Duan-Lu | |
| 2012 | |
| Source | JOURNAL OF MATHEMATICAL PHYSICS
 |
| ISSN | 0022-2488 |
| Volume | 53Issue:7Pages:- |
| English 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 cannot 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 >= 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. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4736842; 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 cannot 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 >= 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. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4736842 |
| Indexed Type | SCI |
| Department | Chen Jianxin; Zeng Bei Univ Guelph Dept Math & Stat Guelph ON N1G 2W1 Canada. Chen Jianxin; Ji Zhengfeng; Ruskai Mary Beth; Zeng Bei Univ Waterloo Inst Quantum Comp Waterloo ON N2L 3G1 Canada. Ji Zhengfeng Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing Peoples R China. Ruskai Mary Beth Tufts Univ Medford MA 02155 USA. Zhou Duan-Lu Chinese Acad Sci Beijing Natl Lab Condensed Matter Phys Beijing 100190 Peoples R China. Zhou Duan-Lu Chinese Acad Sci Inst Phys Beijing 100190 Peoples R China. |
| Subject | Physics |
| Sponsorship | Natural Sciences and Engineering Research Council (Canada) (NSERC); National Science Foundation of China (NSFC) 61179030, 10975181, 11175247; NSERC; U.S. Army Research Office (USARO); National Science Foundation (NSF); Canadian Institute for Advanced Research (CIFAR); National Key Basic Research Special Funds (NKBRSF) of China 2012CB922104 |
| Language | 英语 |
| WOS ID | WOS:000307609900004 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/15077 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Chen Jianxin,Ji Zhengfeng,Ruskai Mary Beth,et al. comment on some results of erdahl and the convex structure of reduced density matrices[J]. JOURNAL OF MATHEMATICAL PHYSICS,2012,53(7):-. |
| APA | Chen Jianxin,Ji Zhengfeng,Ruskai Mary Beth,Zeng Bei,&Zhou Duan-Lu.(2012).comment on some results of erdahl and the convex structure of reduced density matrices.JOURNAL OF MATHEMATICAL PHYSICS,53(7),-. |
| MLA | Chen Jianxin,et al."comment on some results of erdahl and the convex structure of reduced density matrices".JOURNAL OF MATHEMATICAL PHYSICS 53.7(2012):-. |
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