Trace distance measure of coherence for a class of qudit states

Recently, trace distance measure of coherence has been proposed for characterizing the coherence of a given quantum state. However, it seems difficult to estimate the optimal incoherent state for high dimensional states. An explicit expression for the trace distance measure of coherence for a class of qudit states is provided. We show that the closest incoherent state to the class of qudit states is just the diagonal matrix obtained from it by deleting all off-diagonal elements. It is also shown that the measure of coherence induced by trace distance can act as a measure of coherence for this class of qudit states with some restrictions on the strictly incoherent operations.