Masking quantum information in multipartite scenario

Abstract: Recently, Kavan Modi \emph{et al.} found that masking quantum information is impossible in bipartite scenario in [Phys. Rev. Lett. \textbf{120}, 230501 (2018)]. This adds another item of the no-go theorems. In this paper, we present some new schemes different from error correction codes, which show that quantum states can be masked when more participants are allowed in the masking process. Moreover, using a pair of mutually orthogonal Latin squares of dimension $d$, we show that all the $d$ level quantum states can be masked into tripartite quantum systems whose local dimensions are $d$ or $d+1$. This highlight some difference between the no-masking theorem and the classical no-cloning theorem or no-deleting theorem.