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This study proposes a novel QPC protocol that leverages Bell states to ensure data privacy, utilizing the fundamental principles of quantum mechanics. Within this framework, two participants, each possessing a secret integer, encode the binary representation of their values using Pauli-X and Pauli-Z operators applied to quantum states transmitted from a semi-honest third party (TP). The TP, which is bound to protocol compliance and prohibited from colluding with either participant, measures the received sequences to determine the comparison result without accessing the participants\u2019 original inputs. Theoretical analyses and simulations validate the protocol\u2019s strong security, high efficiency, and practical feasibility in quantum computing environments. An advantage of the proposed protocol lies in its optimized utilization of Bell states, which enhances qubit efficiency and experimental practicality. Moreover, the proposed protocol outperforms several existing Bell-state-based QPC schemes in terms of efficiency.<\/jats:p>","DOI":"10.3390\/axioms14080549","type":"journal-article","created":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T13:35:28Z","timestamp":1753191328000},"page":"549","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Two-Party Quantum Private Comparison with Pauli Operators"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-2128-4825","authenticated-orcid":false,"given":"Min","family":"Hou","sequence":"first","affiliation":[{"name":"School of Computer Science, Sichuan University Jinjiang College, Meishan 620860, China"},{"name":"Network and Data Security Key Laboratory of Sichuan Province, University of Electronic Science and Technology of China, Chengdu 610054, China"},{"name":"State Key Laboratory of Cognitive Intelligence, Hefei 230088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Sichuan University Jinjiang College, Meishan 620860, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6323-9420","authenticated-orcid":false,"given":"Shibin","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Artificial Intelligence (CUIT Shuangliu Industrial College), Chengdu University of Information Technology, Chengdu 610225, China"},{"name":"Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1145\/3387108","article-title":"Secure multiparty computation","volume":"64","author":"Lindell","year":"2020","journal-title":"Commun. 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