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Quantum State Recovery Via Environment-assisted Measurement and Weak Measurement

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Abstract

In this paper, we propose a quantum state recovery scheme based on environment assisted measurement with weak measurements and flip operations. Before the decoherence channel the weak measurement and flip operators are applied to gain some information about the state of the system and transfer it to a more robust state. Then we utilize environment assisted measurement and post-flip operations to bring the system as close as possible to its initial state. We illustrate our scheme and compare it with a scheme based on environment assisted measurement and weak measurement reversal in the case of a decoherence channel. We show that the success probability of our proposed scheme is significantly improved for all initial states. The proposed scheme is applicable for recovery of N-qubit state from any type of decoherence with at least one invertible Kraus operator. Also, the explicit formula of total fidelity and success probability for recovery of N-qubit GHZ state are derived.

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Funding

This work was supported by the National Natural Science Foundation of China under grant no. 61973290. The research of JJN has been partially supported by the Agencia Estatal de Investigacion (AEI) of Spain, projects MTM2016-75140-P and PID2020-113275GB-I00 and by the European Fund for Regional Development (FEDER). Also by Xunta de Galicia under grant ED431C 2019/02.

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Authors and Affiliations

  1. Department of Automation, University of Science and Technology of China, Hefei, 230027, China

    Sajede Harraz & Shuang Cong

  2. CITMAga, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto

Authors
  1. Sajede Harraz
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  2. Shuang Cong
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  3. Juan J. Nieto
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Contributions

S.H. conceived and developed the idea of EA-WMF, performed the experiments and analyzed the results. S.C. conceived and supervised the project. J.J.N. discussed the results, and commented on the manuscript.

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Correspondence to Sajede Harraz.

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Harraz, S., Cong, S. & Nieto, J.J. Quantum State Recovery Via Environment-assisted Measurement and Weak Measurement. Int J Theor Phys 61, 140 (2022). https://doi.org/10.1007/s10773-022-05055-4

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