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Estimations of the errors between the evolving states generated by two Hamiltonians with the same initial state

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Abstract

Time evolution of a quantum system is described by Schrödinger equation with initial pure state, or von Neumann equation with initial mixed state. In this paper, we estimate the error between the evolving states generated by two Hamiltonians with the same initial pure state. Secondly, according to the method of operator–vector correspondence, we give a relation of the Schrödinger equation and von Neumann equation and then estimate the error between the evolving states generated by two Hamiltonians with the same initial mixed state.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11771009, 11601300, 11571213) and the Fundamental Research Funds for the Central Universities (GK201703093).

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Authors and Affiliations

  1. School of Ethnic Education, Shaanxi Normal University, Xi’an, 710062, China

    Wen-hua Wang

  2. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China

    Huai-xin Cao & Zheng-li Chen

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  1. Wen-hua Wang
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  2. Huai-xin Cao
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  3. Zheng-li Chen
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Correspondence to Huai-xin Cao.

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Wang, Wh., Cao, Hx. & Chen, Zl. Estimations of the errors between the evolving states generated by two Hamiltonians with the same initial state. Quantum Inf Process 17, 21 (2018). https://doi.org/10.1007/s11128-017-1772-y

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