Abstract
Deterministic secure quantum communication (DSQC) is an important primitive of quantum cryptography and has attracted continuous attention. Here, we report the first DSQC protocol based on spatial encoding. The qubit information is encoded in the spatial-mode degree of freedom of photons. A decoy state technique is used to ensure the security of the DSQC protocol. We also analyze the security of the DSQC protocol and show that it is secure against common attacks such as the interception-and-retransmission attack and general entanglement–measurement attack. Without the use of the polarization state of photons, it avoids the degeneration of the states of photons so that it is suitable for long-distance quantum communication.

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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 62071015, 62171264); the China Social Security Foundation (No. 6009258).
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Li, J., Yang, YG., Li, J. et al. Deterministic secure quantum communication based on spatial encoding. Quantum Inf Process 21, 2 (2022). https://doi.org/10.1007/s11128-021-03330-7
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DOI: https://doi.org/10.1007/s11128-021-03330-7