Fidelity induced distance measures for quantum states
  Fidelity plays an important role in quantum information theory. In this letter, we introduce new metric of quantum states induced by fidelity, and connect it with the well-known trace metric, Sine metric and Bures metric for the qubit case. The metric character is also presented for the qudit (i.e., $d$-dimensional system) case. The CPT contractive property and joint convex property of the metric are also studied. 
Zhihao Ma, Fu-Lin Zhang, and Jing-Ling Chen