Quantum Strassen's theorem

doi:10.1142/S0219025720500204

	Quantum Strassen's theorem
	Friedland, Shmuel 1; Ge, Jingtong 2,4; Zhi, Lihong 2,3
刊名	INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS
	2020-09-01
卷号	23 期号:3 页码:29
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
ISSN号	0219-0257
DOI	10.1142/S0219025720500204
英文摘要	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.
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
语种	英语
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
WOS记录号	WOS:000607113000004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/57961]
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.Chinese Acad Sci, KLMM, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Univ Technol Sydney, Sydney, NSW, Australia
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.