We report a new metric of quantum states. This metric is build up from super-fidelity, which has deep connection with the Uhlmann-Jozsa fidelity and plays an important role in quantifying entanglement. We find that the new metric possess some interesting properties.
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 metri
c 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.
In this paper, we study metrics of quantum states. These metrics are natural generalization of trace metric and Bures metric. We will prove that the metrics are joint convex and contractive under quantum operation. Our results can find important appl
ication in studying the geometry of quantum states and is useful to detect entanglement.
