Large Deviation Analysis for Quantum Security via Smoothing of Rényi Entropy of Order 2

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 universal₂ hash functions. Using the smoothing of Rényi entropy of order 2, we derive security bounds for L₁ 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 ε-almost dual universal₂ hash functions. Furthermore, we apply this analysis to the secret key generation with error correction.