ITP OpenIR  > 理论物理所科研产出  > SCI论文
Zhang, Yong; Kauffman, Louis H.; Werner, Reinhard F.; Zhang, Y , Chinese Acad Sci, Inst Theoret Phys, PO Box 2735, Beijing 100080, Peoples R China
Permutation and its partial transpose
发表期刊INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
关键词Universal Quantum Gates Temperley-lieb Algebra Yang-baxterization Virtual Knot Polynomial Invariant Link Polynomials Forbidden Moves Braid-groups Model Separability
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.
2007
ISSN0219-7499
卷号5期号:4页码:469-507
学科领域Physics
收录类别SCI
引用统计
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
专题理论物理所科研产出_SCI论文
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, 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.
条目包含的文件
文件名称/大小 文献类型 版本类型 开放类型 使用许可
Permutation and its (408KB) 开放获取使用许可请求全文
个性服务
推荐该条目
保存到收藏夹
查看访问统计
导出为Endnote文件
谷歌学术
谷歌学术中相似的文章
[Zhang, Yong]的文章
[Kauffman, Louis H.]的文章
[Werner, Reinhard F.]的文章
百度学术
百度学术中相似的文章
[Zhang, Yong]的文章
[Kauffman, Louis H.]的文章
[Werner, Reinhard F.]的文章
必应学术
必应学术中相似的文章
[Zhang, Yong]的文章
[Kauffman, Louis H.]的文章
[Werner, Reinhard F.]的文章
相关权益政策
暂无数据
收藏/分享
所有评论 (0)
暂无评论
 

除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。