{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T19:18:30Z","timestamp":1781032710666,"version":"3.54.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2025,7,21]],"date-time":"2025-07-21T00:00:00Z","timestamp":1753056000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,21]],"date-time":"2025-07-21T00:00:00Z","timestamp":1753056000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62202017"],"award-info":[{"award-number":["62202017"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62202017"],"award-info":[{"award-number":["62202017"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-025-04835-1","type":"journal-article","created":{"date-parts":[[2025,7,21]],"date-time":"2025-07-21T06:57:16Z","timestamp":1753081036000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Publicly verifiable quantum homomorphic encryption based on quantum remote control"],"prefix":"10.1007","volume":"24","author":[{"given":"Xinglan","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunxin","family":"Xi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,7,21]]},"reference":[{"issue":"11","key":"4835_CR1","first-page":"169","volume":"4","author":"RL Rivest","year":"1978","unstructured":"Rivest, R.L., Adleman, L., Dertouzos, M.L., et al.: On data banks and privacy homomorphisms. Found. Secure Comput. 4(11), 169\u2013180 (1978)","journal-title":"Found. Secure Comput."},{"key":"4835_CR2","doi-asserted-by":"crossref","unstructured":"Ajtai, M.: Generating hard instances of lattice problems. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 99\u2013108 (1996)","DOI":"10.1145\/237814.237838"},{"key":"4835_CR3","doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the Forty-first Annual ACM Symposium on Theory of Computing, pp. 169\u2013178 (2009)","DOI":"10.1145\/1536414.1536440"},{"key":"4835_CR4","doi-asserted-by":"crossref","unstructured":"Goldwasser, S., Kalai, Y., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: Reusable garbled circuits and succinct functional encryption. In: Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp. 555\u2013564 (2013)","DOI":"10.1145\/2488608.2488678"},{"issue":"3","key":"4835_CR5","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1137\/14095772X","volume":"45","author":"S Garg","year":"2016","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. SIAM J. Comput. 45(3), 882\u2013929 (2016)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"4835_CR6","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1137\/120868669","volume":"43","author":"Z Brakerski","year":"2014","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) lwe. SIAM J. Comput. 43(2), 831\u2013871 (2014)","journal-title":"SIAM J. Comput."},{"issue":"6","key":"4835_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1568318.1568324","volume":"56","author":"O Regev","year":"2009","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM (JACM) 56(6), 1\u201340 (2009)","journal-title":"J. ACM (JACM)"},{"key":"4835_CR8","doi-asserted-by":"crossref","unstructured":"Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Advances in Cryptology\u2013CRYPTO 2013: 33rd Annual Cryptology Conference, Santa Barbara, CA, USA, August 18\u201322, 2013. Proceedings, Part I, pp. 75\u201392 . Springer (2013)","DOI":"10.1007\/978-3-642-40041-4_5"},{"issue":"4","key":"4835_CR9","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","volume":"28","author":"CE Shannon","year":"1949","unstructured":"Shannon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656\u2013715 (1949)","journal-title":"Bell Syst. Tech. J."},{"key":"4835_CR10","doi-asserted-by":"crossref","unstructured":"Kushilevitz, E., Ostrovsky, R.: Replication is not needed: single database, computationally-private information retrieval. In: Proceedings 38th Annual Symposium on Foundations of Computer Science, pp. 364\u2013373. IEEE (1997)","DOI":"10.1109\/SFCS.1997.646125"},{"key":"4835_CR11","doi-asserted-by":"crossref","unstructured":"Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124\u2013134. IEEE (1994)","DOI":"10.1109\/SFCS.1994.365700"},{"key":"4835_CR12","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"issue":"15","key":"4835_CR13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.103.150502","volume":"103","author":"AW Harrow","year":"2009","unstructured":"Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103(15), 150502 (2009)","journal-title":"Phys. Rev. Lett."},{"issue":"9","key":"4835_CR14","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1038\/nphys3029","volume":"10","author":"S Lloyd","year":"2014","unstructured":"Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10(9), 631\u2013633 (2014)","journal-title":"Nat. Phys."},{"issue":"7779","key":"4835_CR15","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1038\/s41586-019-1666-5","volume":"574","author":"F Arute","year":"2019","unstructured":"Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., Brandao, F.G., Buell, D.A., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505\u2013510 (2019)","journal-title":"Nature"},{"issue":"15","key":"4835_CR16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.109.150501","volume":"109","author":"PP Rohde","year":"2012","unstructured":"Rohde, P.P., Fitzsimons, J.F., Gilchrist, A.: Quantum walks with encrypted data. Phys. Rev. Lett. 109(15), 150501 (2012)","journal-title":"Phys. Rev. Lett."},{"issue":"12","key":"4835_CR17","doi-asserted-by":"publisher","first-page":"3675","DOI":"10.1007\/s11128-013-0626-5","volume":"12","author":"M Liang","year":"2013","unstructured":"Liang, M.: Symmetric quantum fully homomorphic encryption with perfect security. Quantum Inf. Process. 12(12), 3675\u20133687 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"8","key":"4835_CR18","doi-asserted-by":"publisher","first-page":"2749","DOI":"10.1007\/s11128-015-1034-9","volume":"14","author":"M Liang","year":"2015","unstructured":"Liang, M.: Quantum fully homomorphic encryption scheme based on universal quantum circuit. Quantum Inf. Process. 14(8), 2749\u20132759 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"4835_CR19","doi-asserted-by":"publisher","first-page":"33467","DOI":"10.1038\/srep33467","volume":"6","author":"S-H Tan","year":"2016","unstructured":"Tan, S.-H., Kettlewell, J.A., Ouyang, Y., Chen, L., Fitzsimons, J.F.: A quantum approach to homomorphic encryption. Sci. Rep. 6(1), 33467 (2016)","journal-title":"Sci. Rep."},{"key":"4835_CR20","unstructured":"Lai, C.-Y., Chung, K.-M.: On statistically-secure quantum homomorphic encryption. arXiv:1705.00139 (2017)"},{"issue":"4","key":"4835_CR21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.042334","volume":"98","author":"Y Ouyang","year":"2018","unstructured":"Ouyang, Y., Tan, S.-H., Fitzsimons, J.F.: Quantum homomorphic encryption from quantum codes. Phys. Rev. A 98(4), 042334 (2018)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"4835_CR22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.013332","volume":"2","author":"Y Ouyang","year":"2020","unstructured":"Ouyang, Y., Tan, S.-H., Fitzsimons, J., Rohde, P.P.: Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security. Phys. Rev. Res. 2(1), 013332 (2020)","journal-title":"Phys. Rev. Res."},{"issue":"1","key":"4835_CR23","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1007\/s11128-019-2529-6","volume":"19","author":"M Liang","year":"2020","unstructured":"Liang, M.: Teleportation-based quantum homomorphic encryption scheme with quasi-compactness and perfect security. Quantum Inf. Process. 19(1), 28 (2020)","journal-title":"Quantum Inf. Process."},{"key":"4835_CR24","doi-asserted-by":"publisher","first-page":"976","DOI":"10.22331\/q-2023-04-13-976","volume":"7","author":"Y Hu","year":"2023","unstructured":"Hu, Y., Ouyang, Y., Tomamichel, M.: Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption. Quantum 7, 976 (2023)","journal-title":"Quantum"},{"key":"4835_CR25","doi-asserted-by":"crossref","unstructured":"Broadbent, A., Jeffery, S.: Quantum homomorphic encryption for circuits of low t-gate complexity. In: Annual Cryptology Conference, pp. 609\u2013629. Springer (2015)","DOI":"10.1007\/978-3-662-48000-7_30"},{"key":"4835_CR26","doi-asserted-by":"crossref","unstructured":"Buhrman, H., Fehr, S., Schaffner, C., Speelman, F.: The garden-hose model. In: Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, pp. 145\u2013158 (2013)","DOI":"10.1145\/2422436.2422455"},{"key":"4835_CR27","doi-asserted-by":"crossref","unstructured":"Dulek, Y., Schaffner, C., Speelman, F.: Quantum homomorphic encryption for polynomial-sized circuits. In: Advances in Cryptology-CRYPTO 2016: 36th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 14\u201318, 2016, Proceedings, Part III 36, pp. 3\u201332. Springer (2016)","DOI":"10.1007\/978-3-662-53015-3_1"},{"issue":"6","key":"4835_CR28","first-page":"18","volume":"52","author":"U Mahadev","year":"2020","unstructured":"Mahadev, U.: Classical homomorphic encryption for quantum circuits. SIAM J. Comput. 52(6), 18\u2013189 (2020)","journal-title":"SIAM J. Comput."},{"key":"4835_CR29","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/j.ins.2019.06.009","volume":"501","author":"X-B Chen","year":"2019","unstructured":"Chen, X.-B., Sun, Y.-R., Xu, G., Yang, Y.-X.: Quantum homomorphic encryption scheme with flexible number of evaluator based on (k, n)-threshold quantum state sharing. Inf. Sci. 501, 172\u2013181 (2019)","journal-title":"Inf. Sci."},{"issue":"1","key":"4835_CR30","volume":"10","author":"WK Tham","year":"2020","unstructured":"Tham, W.K., Ferretti, H., Bonsma-Fisher, K., Brodutch, A., Sanders, B.C., Steinberg, A.M., Jeffery, S.: Experimental demonstration of quantum fully homomorphic encryption with application in a two-party secure protocol. Phys. Rev. X 10(1), 011038 (2020)","journal-title":"Phys. Rev. X"},{"issue":"2","key":"4835_CR31","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ac5acc","volume":"7","author":"Z-W Cheng","year":"2022","unstructured":"Cheng, Z.-W., Chen, X.-B., Xu, G., Chang, Y., Yang, Y., Yang, Y.-X.: A secure crossing two qubits protocol based on quantum homomorphic encryption. Quantum Sci. Technol. 7(2), 025027 (2022)","journal-title":"Quantum Sci. Technol."},{"key":"4835_CR32","doi-asserted-by":"crossref","unstructured":"Li, W., Deng, D.-L.: Quantum delegated and federated learning via quantum homomorphic encryption. Res. Direct. Quantum Technol. 1\u20136 (2024)","DOI":"10.1017\/qut.2025.2.pr1"},{"key":"4835_CR33","doi-asserted-by":"crossref","unstructured":"Li, Q., Quan, J., Shi, J., Zhang, S., Li, X.: Secure delegated variational quantum algorithms. In: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (2024)","DOI":"10.1109\/TCAD.2024.3391690"},{"key":"4835_CR34","doi-asserted-by":"crossref","unstructured":"Broadbent, A., Gutoski, G., Stebila, D.: Quantum one-time programs. In: Annual Cryptology Conference, pp. 344\u2013360. Springer (2013)","DOI":"10.1007\/978-3-642-40084-1_20"},{"key":"4835_CR35","doi-asserted-by":"crossref","unstructured":"Alagic, G., Dulek, Y., Schaffner, C., Speelman, F.: Quantum fully homomorphic encryption with verification. In: International Conference on the Theory and Application of Cryptology and Information Security, pp. 438\u2013467. Springer (2017)","DOI":"10.1007\/978-3-319-70694-8_16"},{"key":"4835_CR36","unstructured":"Broadbent, A.: How to verify a quantum computation. arXiv:1509.09180 (2015)"},{"issue":"4","key":"4835_CR37","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ad7a9c","volume":"9","author":"R He","year":"2024","unstructured":"He, R., Chen, L., Li, Q., Tan, X., Chen, L.: Verifiable quantum homomorphic encryption based on garbled evaluation. Quantum Sci. Technol. 9(4), 045051 (2024)","journal-title":"Quantum Sci. Technol."},{"issue":"7","key":"4835_CR38","doi-asserted-by":"publisher","first-page":"1323","DOI":"10.1088\/1009-1963\/14\/7\/010","volume":"14","author":"C Li-Bing","year":"2005","unstructured":"Li-Bing, C., Hong, L., Yu-Hua, L.: Implementing remotely a single-qubit rotation operation by three-qubit entanglement. Chin. Phys. 14(7), 1323 (2005)","journal-title":"Chin. Phys."},{"key":"4835_CR39","unstructured":"Aharonov, D., Ben-Or, M., Eban, E., Mahadev, U.: Interactive proofs for quantum computations. arXiv:1704.04487 (2017)"},{"key":"4835_CR40","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1007\/s00224-018-9872-3","volume":"63","author":"A Gheorghiu","year":"2019","unstructured":"Gheorghiu, A., Kapourniotis, T., Kashefi, E.: Verification of quantum computation: an overview of existing approaches. Theory Comput. Syst. 63, 715\u2013808 (2019)","journal-title":"Theory Comput. Syst."},{"key":"4835_CR41","doi-asserted-by":"crossref","unstructured":"Watrous, J.: Quantum computational complexity. arXiv:0804.3401 (2008)","DOI":"10.1007\/978-0-387-30440-3_428"},{"issue":"4","key":"4835_CR42","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/abe29a","volume":"30","author":"S Ma","year":"2021","unstructured":"Ma, S., Zhu, C., Nie, M., Quan, D.: Efficient self-testing system for quantum computations based on permutations. Chin. Phys. B 30(4), 040305 (2021)","journal-title":"Chin. Phys. B"},{"key":"4835_CR43","unstructured":"Gottesman, D.: The heisenberg representation of quantum computers. arXiv preprint quant-ph\/9807006 (1998)"},{"key":"4835_CR44","volume-title":"Quantum Computation and Quantum Information: 10th","author":"MA Nielsen","year":"2010","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th, Anniversary Cambridge University Press, Cambridge (2010)","edition":"Anniversary"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04835-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-04835-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04835-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T16:12:13Z","timestamp":1757261533000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-04835-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,21]]},"references-count":44,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["4835"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-04835-1","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,21]]},"assertion":[{"value":"12 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"231"}}