Determination of locally perfect discrimination for two-qubit unitary operations

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• 作者：Tian-Qing Cao ; Fei Gao ; Ying-Hui Yang ; Zhi-Chao Zhang…
• 关键词：Local discrimination ; Unitary operations ; Local numerical range
• 刊名：Quantum Information Processing
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：15
• 期：1
• 页码：529-549
• 全文大小：901 KB
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• 作者单位：Tian-Qing Cao (1)
  Fei Gao (1)
  Ying-Hui Yang (1) (2)
  Zhi-Chao Zhang (1)
  Qiao-Yan Wen (1)
  
  1. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China
  2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Mathematics
  Engineering, general
  Computer Science, general
  Characterization and Evaluation Materials
  
• 出版者：Springer Netherlands
• ISSN：1573-1332

文摘

In the study of local discrimination for multipartite unitary operations, Duan et al. (Phys Rev Lett 100(2):020503, 2008) exhibited an ingenious expression: Any two different unitary operations \(U_1\) and \(U_2\) are perfectly distinguishable by local operations and classical communication in the single-run scenario if and only if 0 is in the local numerical range of \(U_1^\dag U_2\). However, how to determine when 0 is in the local numerical range remains unclear. So it is generally hard to decide the local discrimination of nonlocal unitary operations with a single run. In this paper, for two-qubit diagonal unitary matrices V and their local unitary equivalent matrices, we present a necessary and sufficient condition for determining whether the local numerical range is a convex set or not. The result can be used to easily judge the locally perfect distinguishability of any two unitary operations \(U_1\) and \(U_2\) satisfying \(U_1^\dag U_2=V\). Moreover, we design the corresponding protocol of local discrimination. Meanwhile, an interesting phenomenon is discovered: Under certain conditions with a single run, \(U_1\) and \(U_2\) such that \(U_1^\dag U_2=V\) are locally distinguishable with certainty if and only if they are perfectly distinguishable by global operations.