Quantum Information Processing

, Volume 14, Issue 2, pp 731–737 | Cite as

Bound on local unambiguous discrimination between multipartite quantum states

  • Ying-Hui Yang
  • Fei Gao
  • Guo-Jing Tian
  • Tian-Qing Cao
  • Hui-Juan Zuo
  • Qiao-Yan Wen


We investigate the upper bound on unambiguous discrimination by local operations and classical communication. We demonstrate that any set of linearly independent multipartite pure quantum states can be locally unambiguously discriminated if the number of states in the set is no more than \(\max \{d_{i}\}\), where the space spanned by the set can be expressed in the irreducible form \(\otimes _{i=1}^{N}d_{i}\) and \(d_{i}\) is the optimal local dimension of the \(i\hbox {th}\) party. That is, \(\max \{d_{i}\}\) is an upper bound. We also show that it is tight, namely there exists a set of \(\max \{d_{i}\}+1\) states, in which at least one of the states cannot be locally unambiguously discriminated. Our result gives the reason why the multiqubit system is the only exception when any three quantum states are locally unambiguously distinguished.


Quantum information Upper bound Unambiguous discrimination Local operations and classical communication  Multipartite quantum states 



The authors would like to thank Runyao Duan for many valuable suggestions. This work is supported by NSFC (Grant Nos. 61300181, 61272057, 61202434, 61170270, 61100203, 61121061, 61402148), Beijing Natural Science Foundation (Grant No. 4122054), Beijing Higher Education Young Elite Teacher Project (Grant Nos. YETP0475, YETP0477), Project of Science and Technology Department of Henan Province of China (142300410143).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Ying-Hui Yang
    • 1
    • 2
  • Fei Gao
    • 1
  • Guo-Jing Tian
    • 1
  • Tian-Qing Cao
    • 1
  • Hui-Juan Zuo
    • 1
    • 3
  • Qiao-Yan Wen
    • 1
  1. 1.State Key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.School of Mathematics and Information ScienceHenan Polytechnic UniversityJiaozuoChina
  3. 3.Mathematics and Information Science CollegeHebei Normal UniversityShijiazhuangChina

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