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The geometric approach to quantum correlations: computability versus reliability

Tufarelli,Tommaso; MacLean,Tom; Girolami,Davide; Vasile,Ruggero; Adesso,Gerardo
Journal of Physics A: Mathematical and Theoretical 46, 275308 (1-15) (2013)

We propose a modified metric based on the Hilbert–Schmidt norm and adopt it to define a rescaled version of the geometric measure of quantum discord. Such a measure is found not to suffer from pathological dependence on state purity. Although the employed metric is still non-contractive under quantum operations, we show that the resulting indicator of quantum correlations is in agreement with other bona fide discord measures in a number of physical examples. We present a critical assessment of the requirements of reliability versus computability when approaching the task of quantifying, or measuring, general quantum correlations in a bipartite state.