Quantum Strassen's theorem

doi:10.1142/S0219025720500204

CSpace

	Quantum Strassen's theorem
	Friedland, Shmuel 1; Ge, Jingtong 2,3; Zhi, Lihong 2,4
	2020-09-01
发表期刊	INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS
ISSN	0219-0257
卷号	23 期号:3 页码:29
摘要	Strassen's theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite, Strassen's theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen's theorem in this case can be stated and solved using semidefinite programming. The aim of this paper is to give analogs of Strassen's theorem to density trace class operators on a product of two separable Hilbert spaces, where at least one of the Hilbert spaces is infinite-dimensional.
关键词	Density matrices and operators quantum marginals quantum couplings trace class operators Hilbert-Schmidt operators partial traces and weak operator convergence SDP problems related to quantum marginals Hausdorff metric
DOI	10.1142/S0219025720500204
收录类别	SCI
语种	英语
资助项目	National Key Research Project of China[2018YFA0306702] ; National Natural Science Foundation of China[12071467]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Quantum Science & Technology ; Physics, Mathematical ; Statistics & Probability
WOS记录号	WOS:000607113000004
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57962
专题	中国科学院数学与系统科学研究院
通讯作者	Zhi, Lihong
作者单位	1.Univ Illinois, Dept Math & Comp Sci, Chicago, IL 60607 USA 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 3.Univ Technol Sydney, Sydney, NSW, Australia 4.Chinese Acad Sci, KLMM, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Friedland, Shmuel,Ge, Jingtong,Zhi, Lihong. Quantum Strassen's theorem[J]. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS,2020,23(3):29.
APA	Friedland, Shmuel,Ge, Jingtong,&Zhi, Lihong.(2020).Quantum Strassen's theorem.INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS,23(3),29.
MLA	Friedland, Shmuel,et al."Quantum Strassen's theorem".INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS 23.3(2020):29.