Abstract
In this paper, using the quantum entanglement swapping technologies under the collective-dephasing noise and the collective-rotation noise, two robust quantum dialogue protocols are proposed, respectively. The logical Bell states are used as the traveling states to combat the collective noise. The auxiliary logical Bell state is shared privately between two participants through the manner of direct transmission first. After encoded with the receiver’s secret messages, it swaps entanglement with its adjacent logical Bell state. In this way, the information leakage problem is avoided. Moreover, Eve’s active attacks can be detected with the help of decoy photon technology. For decoding, the Bell state measurements rather than the four-qubit joint measurements are needed.

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Acknowledgments
The author would like to thank the anonymous reviewers for their valuable suggestions that help enhancing the quality of this paper. Funding by the National Natural Science Foundation of China (Grant Nos. 61402407, 11375152) is also gratefully acknowledged.
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Ye, TY. Robust quantum dialogue based on the entanglement swapping between any two logical Bell states and the shared auxiliary logical Bell state. Quantum Inf Process 14, 1469–1486 (2015). https://doi.org/10.1007/s11128-015-0934-z
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DOI: https://doi.org/10.1007/s11128-015-0934-z