Masking quantum information in multipartite systems via Fourier and Hadamard Matrices

Quantum information masking (QIM) is a crucial technique for protecting quantum data from being accessed by local subsystems. In this paper, we introduce a novel method for achieving 1-uniform QIM in multipartite systems utilizing a Fourier matrix. We further extend this approach to construct an orthogonal array with the aid of a Hadamard matrix, which is a specific type of Fourier matrix. This allows us to explore the relationship between 2-uniform QIM and orthogonal arrays. Through this framework, we derive two distinct 2-uniform quantum states, enabling the 2-uniform masking of original information within multipartite systems. Furthermore, we prove that the maximum number of quantum bits required for achieving a 2-uniformly masked state is 2 n − 1, and the minimum is 2 n −1 + 3. Moreover, our scheme effectively demonstrates the rich quantum correlations between multipartite systems and has potential application value in quantum secret sharing.