A lower bound on the fidelity between two states in terms of their trace-distance and max-relative entropy

Abstract

Fidelity is a fundamental and ubiquitous concept in quantum information theory. Fuchs–van de Graaf’s inequalities deal with bounding fidelity from above and below. In this paper, we give a lower bound on the quantum fidelity between two states in terms of their trace-distance and their max-relative entropy.

Keywords:

• quantum fidelity
• max-relative entropy
• tracenorm
• Fuchs–van de Graaf’s inequalities

Acknowledgements

The authors are grateful to Koenraad M.R. Audenaert for sending us his note and telling us his different approach towards the proof of Theorem 2.2.

Notes

There is no potential conflict of interest.

Additional information

Funding

The work was supported by National Natural Science Foundation of China [11301124], [11171301] and by the Doctoral Programs Foundation of the Ministry of Education of China [J20130061].