We show that trace distance measure of coherence is a strong monotone for all qubit and, so called, X states. An expression for the trace distance coherence for all pure states and a semi definite program for arbitrary states is provided. We also explore the relation between l1-norm and relative entropy based measures of coherence, and give a sharp inequality connecting the two. In addition, it...

We introduce a distance measure based on the idea that two vectors are considered similar if they lead to similar predictive probability distributions. The suggested approach avoids the scaling problem inherent to many alternative techniques as the method automatically transforms the original attribute space to a probability space where all the numbers lie between 0 and 1. The method is also ex...