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

Abstract: 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.