$$n\rightarrow 1$$ n → 1 Quantum random access codes using single 3-level systems

Quantum random access codes (QRACs) have attracted much attention because of their different properties from random access codes. How to explore and verify optimal QRAC strategies is an important research topic in quantum cryptography. In this paper, we focus on optimal $$n\rightarrow 1$$ QRACs using single 3-level systems. Here, we present a general upper bound of maximum guess probability of $$n\rightarrow 1$$ QRACs using a generalized Bloch sphere representation, and the maximum guess probability is an important indicator to verify whether it is the optimal QRAC. Furthermore, the optimal $$2\rightarrow 1$$ and $$3\rightarrow 1$$ QRACs are obtained through analytical methods. Finally, tight upper bounds of the maximum guess probability of $$2\rightarrow 1$$ and $$3\rightarrow 1$$ QRACs are acquired. These results will improve QRAC-based quantum cryptography protocols, such as quantum key distributions, quantum random number generations.