Quantum state tomography for generic pure states

  • ShiLin Huang
  • JianXin Chen
  • YouNing Li
  • Bei ZengEmail author


We examine the problem of whether a multipartite pure quantum state can be uniquely determined by its reduced density matrices. We show that a generic pure state in three party Hilbert space HAHBHC, where dim(HA) = 2 and dim(HB) = dim(HC), can be uniquely determined by its reduced states on subsystems HAHBHC. Then, we generalize the conclusion to the case that dim(H1) > 2. As a corollary, we show that a generic N-qudit pure quantum state is uniquely determined by only two of its \(\left\lceil {\frac{{N + 1}}{2}} \right\rceil \)-particle reduced density matrices. Furthermore, our results indicate a method to uniquely determine a generic N-qudit pure state of dimension D = dN with only O(D) local measurements, which is an improvement compared to the previous known approach that uses O(Dlog2D) or O(Dlog D) local measurements.


state reconstruction quantum tomography foundations of quantum mechanics measurement theory 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • ShiLin Huang
    • 1
  • JianXin Chen
    • 2
  • YouNing Li
    • 3
  • Bei Zeng
    • 4
    • 5
    Email author
  1. 1.Institute for Interdisciplinary Information SciencesTsinghua UniversityBeijingChina
  2. 2.Aliyun Quantum LaboratoryHangzhouChina
  3. 3.Department of Physics and Collaborative Innovation Center of Quantum MatterTsinghua UniversityBeijingChina
  4. 4.Department of Mathematics & StatisticsUniversity of GuelphGuelphCanada
  5. 5.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada

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