Abstract
A closed expression is derived for the amount of resource present in a quantum state as quantified by a distance measure based on the Tsallis relative entropy introduced recently [H. Zhao and C.-s. Yu, Sci. Rep. 8, 299 (2018)], for any resource theory whose set of free states is described by the image of a unital resource-destroying map. By applying it to the resource theory of coherence it is demonstrated that the correct definition of a projective coarse-grained measurement needs to be modified in order for it to be correctly interpreted as a measurement which provides less information about a system's true state than the one obtained from a finer-grained measurement.
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