  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.
