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Permutation and its partial transpose
Zhang, Yong; Kauffman, Louis H.; Werner, Reinhard F.; Zhang, Y , Chinese Acad Sci, Inst Theoret Phys, PO Box 2735, Beijing 100080, Peoples R China
2007
发表期刊INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
ISSN0219-7499
卷号5期号:4页码:469-507
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.
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
关键词Universal Quantum Gates Temperley-lieb Algebra Yang-baxterization Virtual Knot Polynomial Invariant Link Polynomials Forbidden Moves Braid-groups Model Separability
学科领域Physics
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收录类别SCI
WOS记录号WOS:000251175600003
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被引频次:7[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/5682
专题理论物理所1978-2010年知识产出
通讯作者Zhang, Y , Chinese Acad Sci, Inst Theoret Phys, PO Box 2735, Beijing 100080, Peoples R China
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GB/T 7714
Zhang, Yong,Kauffman, Louis H.,Werner, Reinhard F.,et al. Permutation and its partial transpose[J]. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION,2007,5(4):469-507.
APA Zhang, Yong,Kauffman, Louis H.,Werner, Reinhard F.,&Zhang, Y , Chinese Acad Sci, Inst Theoret Phys, PO Box 2735, Beijing 100080, Peoples R China.(2007).Permutation and its partial transpose.INTERNATIONAL JOURNAL OF QUANTUM INFORMATION,5(4),469-507.
MLA Zhang, Yong,et al."Permutation and its partial transpose".INTERNATIONAL JOURNAL OF QUANTUM INFORMATION 5.4(2007):469-507.
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