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题名: Permutation and its partial transpose
作者: Zhang, Yong ;  Kauffman, Louis H. ;  Werner, Reinhard F.
刊名: INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
出版日期: 2007
卷号: 5, 期号:4, 页码:469-507
关键词: UNIVERSAL QUANTUM GATES ;  TEMPERLEY-LIEB ALGEBRA ;  YANG-BAXTERIZATION ;  VIRTUAL KNOT ;  POLYNOMIAL INVARIANT ;  LINK POLYNOMIALS ;  FORBIDDEN MOVES ;  BRAID-GROUPS ;  MODEL ;  SEPARABILITY
学科分类: Physics
通讯作者: Zhang, Y , Chinese Acad Sci, Inst Theoret Phys, PO Box 2735, Beijing 100080, Peoples R China
部门归属: Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China; Univ Utah, Dept Phys, Salt Lake City, UT 84112 USA; Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA; Tech Univ Carolo Wilhelmina Braunschweig, Inst Math Phys, D-38304 Braunschweig, Germany
英文摘要: Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang-Baxter equation, and the isotropic state with an adjustable parameter is found to form a braid representation. The set of permutation's partial transposes is an algebra called the PPT algebra, which guides the construction of multipartite symmetric states. The virtual knot theory, having permutation as a virtual crossing, provides a topological language describing quantum computation as having permutation as a swap gate. In this paper, permutation's partial transpose is identified with an idempotent of the Temperley-Lieb algebra. The algebra generated by permutation and its partial transpose is found to be the Brauer algebra. The linear combinations of identity, permutation and its partial transpose can form various projectors describing tangles; braid representations; virtual braid representations underlying common solutions of the braid relation and Yang-Baxter equations; and virtual Temperley-Lieb algebra which is articulated from the graphical viewpoint. They lead to our drawing a picture called the ABPK diagram describing knot theory in terms of its corresponding algebra, braid group and polynomial invariant. The paper also identifies non-trivial unitary braid representations with universal quantum gates, derives a Hamiltonian to determine the evolution of a universal quantum gate, and further computes the Markov trace in terms of a universal quantum gate for a link invariant to detect linking numbers.
收录类别: SCI
原文出处: 查看原文
WOS记录号: WOS:000251175600003
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内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/5682
Appears in Collections:理论物理所1978-2010年知识产出_期刊论文

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Recommended Citation:
Zhang, Yong,Kauffman, Louis H.,Werner, Reinhard F.. Permutation and its partial transpose[J]. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION,2007,5(4):469-507.
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