Abstract
We revisited the quantum secure direct communication (QSDC) by using a notation (Li et al. in Phys. Lett. A 297:121, 2002; Li et al. in Int. J. Theor. Phys. 46(7):1815, 2007) and generalized QSDC to arbitrary finite dimensions, we also figured out the decoding formula for QSDC of arbitrary finite dimensions. In order to overcome the channel noisy, we present a scheme through introduce n auxilians by using quantum swapping.
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