Masking Quantum Information on Hyperdisks

Masking information is a protocol that encodes quantum information into a bipartite entangled state while the information is completely unknown to local systems. This paper explicitly studies the structure of the set of maskable states and its relation to hyperdisks. We prove that although the qubit states which can be masked must locate on a single hyperdisk, the set of maskable states can consist of two or more hyperdisks for high-dimensional cases. Our results may shed light on several research fields of quantum information theory, such as the structure of entangled states and the local discrimination of bipartite states.