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

TL;DR

This paper develops new quantum privacy amplification theorems based on quantum conditional Rényi entropy, providing precise evaluation of leaked information and asymptotic security rates against quantum eavesdroppers.

Contribution

It introduces novel quantum privacy amplification theorems that improve upon previous results, enabling accurate assessment of leaked information in quantum key distribution.

Findings

Derived exponential decay rate for leaked information.

Established asymptotic equivocation rate in quantum setting.

Provided bounds applicable to quantum eavesdropping scenarios.

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.