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Generalized quantum no-go theorems of pure states

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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.

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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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Authors and Affiliations

  1. Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, 610031, China

    Hui-Ran Li & Ming-Xing Luo

  2. School of Computer and Information Science, Southwest University, Chongqing, 400715, China

    Hong Lai

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  1. Hui-Ran Li
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Correspondence to Ming-Xing Luo.

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Li, HR., Luo, MX. & Lai, H. Generalized quantum no-go theorems of pure states. Quantum Inf Process 17, 168 (2018). https://doi.org/10.1007/s11128-018-1936-4

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