Skew information revisited: Its variants and a comparison of them

Skew information was introduced by Wigner and Yanase in the context of quantum measurements. It was later recognized that skew information in addition to its original significance as a measure of the information content of states admits several interpretations of a more physical and information theory nature. This quantity has now found many applications in quantum information. An intriguing and subtle feature of skew information is the involvement of the square root of quantum states (density operators). Comparing skew information with some of its natural modifications reveals mathematical and also physical reasons for using the square root. We further use skew information to quantify the asymmetry of quantum states with respect to group representations.