International Journal of Theoretical Physics

, Volume 54, Issue 6, pp 2001–2011 | Cite as

Partition a Quantum Pure-state Set into Unambiguously Discriminable Subsets

  • Jianting Wang
  • Jianyu Wang
  • Zhongqian Fu


The problem of partitioning a quantum pure-state set into unambiguously discriminable subsets is investigated in this paper. We prove that the problem is decomposable into sub-problems of two-subset partitioning. A recursive algebro-geometric method based on Generalized Principal Component Analysis(GPCA) is proposed. When multiple feasible partitions exist, our method is able to return all of them by introducing Brill’s equations. Through this method, the efficiency of a kind of collective photon-number-splitting(PNS) attack is discussed.


Unambiguous set discrimination Subspace clustering Collective attack Generalized principal component analysis 



We would thank Prof. René Vidal and Prof. Song Lin for their insightful advices and discussions.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Shanghai Institute of Technical PhysicsChinese Academy of SciencesShanghaiChina
  2. 2.Department of Electronic Science and TechnologyUniversity of Science and Technology of ChinaHefeiChina

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