Strong Converse for Privacy Amplification against Quantum Side Information

We establish a one-shot strong converse bound for privacy amplification against quantum side information with trace distance as a security criterion. Firstly, our result shows that the trace distance converges to 1 exponentially fast for any finite blocklength when the rate of the extractable randomness exceeds the conditional von Neumann entropy of Alice given Eavesdropper. Secondly, we obtain a second-order converse bound for the maximal extractable randomness. Thirdly, our result extends to the moderate deviation regime. Namely, when the rate of the extractable randomness approaches the conditional von Neumann entropy from above with speed slower than $O\left( {1/\sqrt n } \right.$, the trace distance still converges to 1 asymptotically. Lastly, our result yields strong converse to entropy accumulation, which complements the recent result by Dupuis [arXiv:2105.05342]. The full manuscript can be assessed in [1], [2].