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Quantum discord is a manifestation of quantum correlations due to non-commutativity rather than entanglement. Two measures of quantum discord by the amount of non-commutativity via the trace norm and the Hilbert-Schmidt norm respectively are proposed in this paper. These two measures can be calculated easily for any state with arbitrary dimension. It is shown by several examples that these measures can reflect the amount of the original quantum discord. two measures: the trace norm measure anddoi:10.1038/srep25241 pmid:27122226 pmcid:PMC4848517 fatcat:hmf3ufdxfrhebba5ddo3ahzopm