  Unlike quantum correlations, the shareability of classical correlations (CCs)
between two-parties of a multipartite state is assumed to be free since there
exist states for which CCs for each of the reduced states can simultaneously
reach their algebraic maximum value. However, when one randomly picks out
states from the state space, we find that the probability of obtaining those
states possessing the algebraic maximum value is vanishingly small. We explore
the possibility of nontrivial upper bound by Haar uniformly generating random
multipartite states and computing the frequency distribution for various CC
measures, conventional classical correlators, and two axiomatic measures of
classical correlations, namely the classical part of quantum discord and local
work of work-deficit. We find that the distributions are typically
Gaussian-like and their standard deviations decrease with the increase in
number of parties. It also reveals that among the multiqubit random states,
most of the reduced density matrices possess a low amount of CCs which can also
be confirmed by the mean of the distributions, thereby showing a kind of
restrictions on the sharability of classical correlations for random states.
Furthermore, we also notice that the maximal value for random states is much
lower than the algebraic maxima obtained for a set of states, and the gap
between the two increases further for states with a higher number of parties.
We report that for a higher number of parties, the classical part of quantum
discord and local work can follow monogamy-based upper bound on sharability
while classical correlators have a different upper bound. The trends of
sharability for classical correlation measures in random states clearly
demarcate between the axiomatic definition of classical correlations and the
conventional ones.
