  In the commented paper, the authors declare an analogy with the quantum
mechanical pure states established through the application of the
high-dimensional combinatorial Laplacian considering that the simplicial
complex is in the pure state when it is formed by collection of the pure
states. In their work, besides giving a completely erroneous analogy for the
pure quantum mechanical state, which contradicts to very basic postulates of
quantum mechanic, the authors clearly fail to provide and explain mathematical
formalism behind their claims. Their intention is to rigorously prove that the
existence of opinion space in all considered cases consists of the pure quantum
states using incorrect normalization constant which does not produce trace
equal to one. In this comment we prove out that their claims are erroneous. In
order to show incorrectness of Maletic & Rajkovic model and conclusions we
calculated and examined connections between different combinatorial structures
of q- dimensional simplicial complexes and their Laplacian spectra and analyzed
resulting symmetric and positive semidefinite matrices in the context of the
density matrix of a quantum mechanical system. Importance of presented research
is to further develop accurate quantitative topological-based characterization
method for convertibility and distillation of density matrix.
