This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities, the authors establish tighter bounds for information-theoretic security, demonstrating that quantum protocols inherently outperform classical counterparts in balancing privacy and efficiency. Also explores symmetric Quantum Private Information Retrieval (QPIR) protocols that achieve sub-linear communication complexity while ensuring robustness against specious adversaries: A post-quantum cryptography based protocol that can be authenticated for the specious server; A ring-LWE-based protocol for post-quantum security in a single-server setting, ensuring robustness against quantum attacks; A multi-server protocol optimized for hardware practicality, reducing implementation overhead while maintaining sub-linear efficiency. These protocols address critical gaps in secure database queries, offering exponential communication improvements over classical linear-complexity methods. The work also analyzes security trade-offs under quantum specious adversaries, providing theoretical guarantees for privacy and correctness.
View on arXiv@article{liu2025_2504.04041,
title={ Authenticated Sublinear Quantum Private Information Retrieval },
author={ Fengxia Liu and Zhiyong Zheng and Kun Tian and Yi Zhang and Heng Guo and Zhe Hu and Oleksiy Zhedanov and Zixian Gong },
journal={arXiv preprint arXiv:2504.04041},
year={ 2025 }
}