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Generalized quantum no-go theorems of pure states

  • Hui-Ran Li
  • Ming-Xing Luo
  • Hong Lai
Article

Abstract

Various results of the no-cloning theorem, no-deleting theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. First, we prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes the no-cloning theorem, no-anticloning theorem, no-partial-erasure theorem, no-splitting theorem, no-superposing theorem or no-encoding theorem as a special case. Moreover, it implies various new results. Third, we extend the new theorem into another form that includes the no-deleting theorem as a special case.

Keywords

Quantum no-go theorem Generalized no-go theorem Quantum no-superposing theorem Pure state 

Notes

Acknowledgements

We thank Luming Duan and Yaoyun Shi. This work was supported by the National Natural Science Foundation of China (Nos. 61772437, 61702427), Sichuan Youth Science and Technique Foundation (No. 2017JQ0048) and Fundamental Research Funds for the Central Universities (No. XDJK2016C043), Chuying Fellowship and the Doctoral Program of Higher Education (No. SWU115091).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Information Security and National Computing Grid LaboratorySouthwest Jiaotong UniversityChengduChina
  2. 2.School of Computer and Information ScienceSouthwest UniversityChongqingChina

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