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-norm distance and their max-relative entropy.

v1: 6 pages, no figure, any comments are welcome! v2:Some little errors are corrected. The third author is included. v3: Some minor revisions are made. arXiv admin note: text overlap with arXiv:1309.6374

References in corpus (4)

• Robust Quantum Error Correction via Convex Optimization
• Quantum Skew Divergence
• Transition Probability (Fidelity) and Its Relatives
• A lower bound on the fidelity between two states in terms of their Bures distance

Cited by in corpus (3)

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• Quantum Rényi and $f$-divergences from integral representations
• Contraction of Private Quantum Channels and Private Quantum Hypothesis Testing