Optimal approximations of available states and a triple uncertainty relation

Xiao-Bin Liang, Bo Li, Liang Huang, Biao-Liang Ye, Shao-Ming Fei, and Shi-Xiang Huang
Phys. Rev. A 101, 062106 – Published 9 June 2020

Abstract

We investigate the optimal convex approximation of the quantum state with respect to a set of available states. By isometric transformation, we have presented the general mathematical model and its solutions together with a triple uncertainty equality relation. Meanwhile, we show a concise inequality criterion for decomposing qubit mixed states. The new results include previous ones as special cases. Our model and method may be applied to solve similar problems in high-dimensional and multipartite scenarios.

  • Received 22 December 2019
  • Accepted 22 May 2020

DOI:https://doi.org/10.1103/PhysRevA.101.062106

©2020 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Quantum Information, Science & TechnologyAtomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Xiao-Bin Liang1,*, Bo Li1,†, Liang Huang2, Biao-Liang Ye3, Shao-Ming Fei4,5,‡, and Shi-Xiang Huang1,§

  • 1School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001, China
  • 2Department of Computer and Software Engineering, Wonkwang University, Iksan 54538, Korea
  • 3Quantum Information Research Center, Shangrao Normal University, Shangrao 334001, China
  • 4School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 5Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany

  • *liangxiaobin2004@126.com
  • libobeijing2008@163.com
  • feishm@cnu.edu.cn
  • §hsx8154562@126.com

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Issue

Vol. 101, Iss. 6 — June 2020

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