  Masking of quantum information means that information is hidden from a
subsystem 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 of
nonorthogonal quantum states and it is not possible for arbitrary quantum
states. In this paper, we discuss the problem of masking quantum information
encoded in pure and mixed states, respectively. Based on an established
necessary and sufficient condition for a set of pure states to be masked by an
operator, we find that there exists a set of four states that can not be
masked, which implies that to mask unknown pure states is impossible. We
construct a masker $S^\sharp$ and obtain its maximal maskable set, leading to
an affirmative answer to a conjecture proposed in Modi's paper mentioned above.
We also prove that an orthogonal (resp. linearly independent) subset of pure
states can be masked by an isometry (resp. injection). Generalizing the case of
pure states, we introduce the maskability of a set of mixed states and prove
that 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 any
operator. We also find the maximal maskable sets of mixed states of the
isometries ${S^{\sharp}}$ and ${S^{\diamond}}$, respectively.
