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Masking of quantum information means that information is hidden from asubsystem and spread over a composite system. Modi et al. proved in [Phys. Rev.Lett. 120, 230501 (2018)] that this is true for some restricted sets ofnonorthogonal quantum states and it is not possible for arbitrary quantumstates. In this paper, we discuss the problem of masking quantum informationencoded in pure and mixed states, respectively. Based on an establishednecessary and sufficient condition for a set of pure states to be masked by anoperator, we find that there exists a set of four states that can not bemasked, which implies that to mask unknown pure states is impossible. Weconstruct a masker $S^\sharp$ and obtain its maximal maskable set, leading toan affirmative answer to a conjecture proposed in Modi's paper mentioned above.We also prove that an orthogonal (resp. linearly independent) subset of purestates can be masked by an isometry (resp. injection). Generalizing the case ofpure states, we introduce the maskability of a set of mixed states and provethat a commuting subset of mixed states can be masked by an isometry$S^{\diamond}$ while it is impossible to mask all of mixed states by anyoperator. We also find the maximal maskable sets of mixed states of theisometries ${S^{\sharp}}$ and ${S^{\diamond}}$, respectively.

Masking quantum information encoded in pure and mixed states