Hat problem: a new strategy based on quantum stabilizer codes

The hat problem has been investigated in plenty of papers and has become a hot mathematical topic. In this paper, we will investigate the hat problem by employing quantum stabilizer code and classical Hamming code. On the one hand, a new strategy is proposed in this paper by utilizing higher-dimensional quantum stabilizer code, which, to the best of our knowledge, can be considered as a new approach to work around that problem for the first time. The solvability of the hat problem is no longer a matter of a hat game for each participant. However, it is simplified into a question about the information detected and corrected through the quantum network. On the other hand, we have performed a detailed feasibility analysis through a series of theorems in quantum space and established the implementation process with an example. Furthermore, our strategy can be applied to a variant of the more general hat problem and approximated to the optimal winning probability.