  Masking quantum information, which is impossible without randomness as a
resource, is a task that encodes quantum information into bipartite quantum
state while forbidding local parties from accessing to that information. In
this work, we disprove the geometric conjecture about unitarily maskable states
[K. Modi et al., Phys. Rev. Lett. 120, 230501 (2018)], and make an algebraic
analysis of quantum masking. First, we show a general result on quantum channel
mixing that a subchannel's mixing probability should be suppressed if its
classical capacity is larger than the mixed channel's capacity. This constraint
combined with the well-known information conservation law, a law that does not
exist in classical information theory, gives a lower bound of randomness cost
of masking quantum information as a monotone decreasing function of evenness of
information distribution. This result provides a consistency test for various
scenarios of fast scrambling conjecture on the black hole evaporation process.
The results given here are robust to incompleteness of quantum masking.
