Quantumness and the role of locality on quantum correlations

Quantum correlations in a physical system are usually studied with respect to a unique (fixed) decomposition of the system into subsystems, without fully exploiting the rich structure of the state-space. Here, we show several examples in which the consideration of different ways to decompose a physical system enhances the quantum resources and accounts for a more flexible definition of quantumness-measures. Furthermore, we give a new perspective regarding how to reassess the fact that local operations play a key role in general quantumness-measures that go beyond entanglement --as discord-like ones. We propose a way to quantify the maximum quantumness of a given state. Applying our definition to low-dimensional bipartite states, we show that different behaviours are reported for separable and entangled states than those corresponding to the usual measures of quantum correlations. We show that there is a close link between our proposal and the criterion to witness quantum correlations based on the rank of the correlation matrix, proposed by Daki\'c, Vedral and Brukner.