It is impossible to mask an arbitrary quantum state into the correlations between two subsystems such that the original information is completely unknown to each local system. This is the no-masking theorem proposed by Modi et al. [K. Modi, A. K. Pati, A. Sen(De), and U. Sen, Phys. Rev. Lett. 120, 230501 (2018)]. In this work, we propose the concept of $k$-uniform quantum information masking in multipartite systems and indicate the relation between quantum error-correcting codes (QECCs) in heterogeneous systems and quantum information masking. As a consequence, we show that the no-masking theorem is a special case of the quantum Singleton bound for QECCs in heterogeneous systems essentially, and we give a more general no-masking theorem in multipartite systems based on the quantum Singleton bound. We also solve two open questions proposed by Li and Wang [M.-S. Li and Y.-L. Wang, Phys. Rev. A 98, 062306 (2018)]. That is, an arbitrary state of level $d$ cannot be masked in a tripartite system of level $d$ such that the marginal states are not proportional to identity, and an arbitrary state of level $d$ cannot be masked in a tripartite system of level $n$ with $n<d$. Further, we give some methods for constructing new QECCs from old QECCs in heterogeneous systems.

• Received 31 May 2021
• Accepted 13 August 2021

DOI:https://doi.org/10.1103/PhysRevA.104.032601