Permutation and its partial transpose

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	Permutation and its partial transpose
	Zhang, Y , Chinese Acad Sci, Inst Theoret Phys, PO Box 2735, Beijing 100080, Peoples R China; Zhang, Yong; Kauffman, Louis H.; Werner, Reinhard F.
刊名	INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
	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
ISSN号	0219-7499
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.
学科主题	Physics
URL标识	查看原文
WOS记录号	WOS:000251175600003
公开日期	2012-08-02
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/5682]
专题	理论物理研究所_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
推荐引用方式 GB/T 7714	Zhang, Y , Chinese Acad Sci, Inst Theoret Phys, PO Box 2735, Beijing 100080, Peoples R China,Zhang, Yong,Kauffman, Louis H.,et al. Permutation and its partial transpose[J]. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION,2007,5(4):469-507.
APA	Zhang, Y , Chinese Acad Sci, Inst Theoret Phys, PO Box 2735, Beijing 100080, Peoples R China,Zhang, Yong,Kauffman, Louis H.,&Werner, Reinhard F..(2007).Permutation and its partial transpose.INTERNATIONAL JOURNAL OF QUANTUM INFORMATION,5(4),469-507.
MLA	Zhang, Y , Chinese Acad Sci, Inst Theoret Phys, PO Box 2735, Beijing 100080, Peoples R China,et al."Permutation and its partial transpose".INTERNATIONAL JOURNAL OF QUANTUM INFORMATION 5.4(2007):469-507.