Large deviation analysis for quantum security via smoothing of Renyi entropy of order 2

Abstract

It is known that the security evaluation can be done by smoothing of Rényi entropy of order 2 in the classical and quantum settings when we apply universal${}_2$ hash functions. Using the smoothing of Renyi entropy of order 2, we derive security bounds for $L_1$ distinguishability and modified mutual information criterion under the classical and quantum setting, and have derived these exponential decreasing rates. These results are extended to the case when we apply $\epsilon$-almost dual universal${}_2$ hash functions. Further, we apply this analysis to the secret key generation with error correction.

The results for the classical case have been removed. This part was moved to the recent paper arXiv:1309.1596

References in corpus (6)

• Distillation of secret key and entanglement from quantum states
• On quantum Renyi entropies: a new generalization and some properties
• Leftover Hashing Against Quantum Side Information
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Upper bounds of eavesdropper's performances in finite-length code with decoy method

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