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Representing expectation values of projectors as series for evolution reconstruction

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Abstract

We propose a Hamiltonian-independent approach for evolution reconstruction, which reconstructs the density operator of an evolving quantum system on the basis of recovering its time-varying expectation values of projectors. We represent band-limited expectation values of projectors as series, in which the coefficient of each term is a sum of an infinite set of measurement results. Both of the series for multiple measurement records and for a single record are given. We demonstrate using them to recover an expectation value and reconstruct the density operator of an evolving two-dimensional quantum system. The theoretical and simulative results prove that the two series are effective when performing a small number of measurements. Our approach is applicable to any quantum system of countable dimensions with arbitrary Hamiltonian.

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Acknowledgments

The authors would like to thank Dr. Mingxi Guo for clarifying discussions. This work was supported by the National Natural Science Foundation of China (Nos. 11404407 and 61371121) and the Natural Science Foundation of Jiangsu Province (No. BK20140072).

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Authors and Affiliations

  1. Institute of Communications Engineering, PLA University of Science and Technology, Haifu Lane No.1, Nanjing, 210007, China

    Hua Zhou,  Rong Wang, Yong Zhu, Yang Su, Zhiyong Xu, Jingyuan Wang, Huiping Shen, Jianhua Li, Peng Xiang & Baofu Zhang

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  1. Hua Zhou
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  2. Rong Wang
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  3. Yong Zhu
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  4. Yang Su
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  5. Zhiyong Xu
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  6. Jingyuan Wang
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  10. Baofu Zhang
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Correspondence to Hua Zhou.

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Zhou, H., Wang, ., Zhu, Y. et al. Representing expectation values of projectors as series for evolution reconstruction. Quantum Inf Process 15, 5155–5165 (2016). https://doi.org/10.1007/s11128-016-1446-1

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