<p>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. This paper also explores several symmetric Quantum Private Information Retrieval (QPIR) protocols that achieve sublinear communication complexity while ensuring robustness against specious adversaries: (i) a post-quantum cryptography-based protocol that can be authenticated for the specious server; (ii) a homomorphic encryption-based protocol in a single-server setting, ensuring robustness against quantum attacks; (iii) a multi-server protocol optimized for hardware practicality, reducing implementation overhead while maintaining sublinear 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.</p>