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There are at least a number of ways to formally define complexity. Most ofthem relate to some kind of minimal description of the studied object. Beingthis one in form of minimal resources of minimal effort needed to generate theobject itself. This is usually achieved by detecting and taking advantage ofregularities within the object. Regularities can commonly be described in aninformation-theoretic approach by quantifying the amount of correlation playinga role in the system, this being spatial, temporal or both. This is theapproach closely related to the extent that the whole cannot be understood asonly the sum of its parts, but also by their interactions. Feature consideredto be most fundamental. Nevertheless, this irreducibility, even in the basicquantum informational setting of composite states, is also present due to theintrinsic structure of Hilbert spaces' tensor product. In this approach, thisirreducibility is quantified based on statistics of von Neumann measurementsforming mutually unbiased bases. Upon two different kinds of tripartite qubitmixed state families, which hold the two possible distinct entangled states onthis space. Results show that this quantification is sensible to the differentkind of entanglement present on those families.

Classical Hierarchical Correlation Quantification on Tripartite Qubit Mixed State Families