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Quantum discord is a measure of quantum correlations beyond theentanglement-separability paradigm. It is conceptualized by using the vonNeumann entropy as a measure of disorder. We introduce a class of quantumcorrelation measures as differences between total and classical correlations,in a shared quantum state, in terms of the sandwiched relative R\'{e}nyi andTsallis entropies. We compare our results with those obtained by using thetraditional relative entropies. We find that the measures satisfy all theplausible axioms for quantum correlations. We evaluate the measures for sharedpure as well as paradigmatic classes of mixed states. We show that the measurescan faithfully detect the quantum critical point in the transverse quantumIsing model and find that they can be used to remove an unquieting feature ofnearest-neighbor quantum discord in this respect. Furthermore, the measuresprovide better finite-size scaling exponents of the quantum critical point thanthe ones for other known order parameters, including entanglement andinformation-theoretic measures of quantum correlations.

Quantum Correlation with Sandwiched Relative Entropies: Advantageous as Order Parameter in Quantum Phase Transitions