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Conventionally, the total correlations within a quantum system are quantifiedthrough distance-based expressions such as the relative entropy or thesquare-norm. Those expressions imply that a quantum state can contain bothclassical and quantum correlations. In this work, we provide an alternativemethod to quantify the total correlations through the Pearson correlationcoefficient. Using this method, we argue that a quantum state can be correlatedin either a classical or a quantum way, i.e., the two cases are mutuallyexclusive. We also illustrate that, at least for the case of two-qubit systems,the distribution of the correlations among certain locally incompatible pairsof observables provides insight in regards to whether a system containsclassical or quantum correlations. Finally, we show how correlations in quantumsystems are connected to the general entropic uncertainty principle.

Quantifying total correlations in quantum systems through the Pearson correlation coefficient