Some New Metrics Based on Partial Fidelity and Partial Super-Fidelity

Zhaoqi Wu, Chuanxi Zhu, Xiaozhi Zhang

In this paper, we introduce some new metrics between quantum states based on partial fidelity and partial super-fidelity and discuss their properties. We show that the new metrics are useful measures in quantum information processing.

C. L. Liu, Da-Jian Zhang, Xiao-Dong Yu +2 more

Zhihua Chen, Zhihao Ma, Fulin Zhang +1 more

Abstract We report a new metric of quantum states. This metric is built up from super-fidelity, which has a deep connection with the Uhlmann-Jozsa fidelity and plays an important role in quantum information processing. We find that the new metric possesses some interesting properties.

Tao Zhou, Yuan Li

In this paper, we give the definition of k th sub-fidelity and k th super-fidelity between quantum states ρ and ϱ, and investigate the relationship among k th partial fidelity ( F k (ρ, ϱ)), k th sub-fidelity ( E k (ρ, ϱ)) and k th super-fidelity ( G k (ρ, ϱ)). In particular, it is shown that E k (ρ, ϱ) ⩽ F k (ρ, ϱ) ⩽ G k (ρ, ϱ). In addition, we show that the partial super-fidelity is a super-multiplicative map, which is G kl (ρ 1 ⊗ϱ 1 , ρ 2 ⊗ϱ 2 ) ⩾ G k (ρ 1 , ρ 2 ) G l (ϱ 1 , ϱ 2 ), for 1 ⩽ k , l ⩽ d .

Oliver Keszöcze, Mathias Soeken, Rolf Drechsler