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

Understand

It is known that the security evaluation can be done by smoothing of R\'{e}nyi 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 $\varepsilon$-almost dual universal$_2$ hash functions.
• Further, we apply this analysis to the secret key generation with error correction.