Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (1): 1-8.

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Ranks of Quantum States with Prescribed Reduced States in an Infinite Dimensional Quantum System

Shuyuan Yang1,3(),Kan He2,3,*()   

  1. 1 College of Information and Computer, Taiyuan University of Technology, Taiyuan 030024
    2 Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026
    3 College of Mathematics, Taiyuan University of Technology, Taiyuan 030024
  • Received:2021-01-27 Online:2022-02-01 Published:2022-02-23
  • Contact: Kan He E-mail:yangshuyuan2000@163.com;hekanquantum@163.com
  • Supported by:
    the NSFC(11771011);the NSFC(12071336);the Key Laboratory of Quantum Information, University of Science and Technology of China

Abstract:

Suppose that $ H$ and $K $ are two infinite dimensional quantum systems (i.e. infinite dimensional complex Hilbert space). Let $\rho $ be a quantum state on $ H\otimes K$ with two reduced states $tr_H(\rho) $ and $ tr_K(\rho)$. Then all possible ranks of $\rho $ are determined in this paper.

Key words: Quantum state, Reduced state, Partial trace, Rank

CLC Number: 

  • O177.1
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