Precise evaluation of leaked information with universal2 privacy amplification in the presence of quantum attacker

We treat secret key extraction when the eavesdropper has correlated quantum states. We propose quantum privacy amplification theorems different from Renner's, which are based on quantum conditional R\'{e}nyi entropy of order 1+s. Using those theorems, we derive an exponential decreasing rate for leaked information and the asymptotic equivocation rate, which have not been derived hitherto in the quantum setting.