Informational distance on quantum-state space

The quantum analog on the quantum state space consisting of all density operators was introduced by generalizing the classical Hellinger distance and affinity on the space of probability densities. The Hellinger distance and affinity with the Bures distance and fidelity were compared and a variety of their fundamental properties were established. A statistical distance which was the same as the affinity in order to quantifying the discrimination of quantum states was introduced. The distances were applied to characterize entanglement and some unusual uncertainty relations nonsimultaneous measurements of a single observable in two different quantum states were established.