  A family of skew information quantities is obtained, in which the well-known
Wigner-Yanase skew information and quantum Fisher information stand as special
cases. A transparent proof of convexity of the generalized skew information is
given, implying a simple proof of the Wigner-Yanase-Dyson conjecture. We find
in this work an exact skew information inequality for qubit system, which may
regard as the information counterpart of the uncertainty relation. A lower
bound for generalized skew information of a pair of incompatible observables in
arbitrary dimension and also the upper bound for qubit system are achieved.
