{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,29]],"date-time":"2025-11-29T15:56:29Z","timestamp":1764431789505,"version":"build-2065373602"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T00:00:00Z","timestamp":1759104000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T00:00:00Z","timestamp":1759104000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["23K10980"],"award-info":[{"award-number":["23K10980"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    For a quantum secret sharing scheme built from a general quantum stabilizer code, no measurement-free circuit has been known for reconstructing its quantum secrets, except particular classes, such as one proposed by Cleve, Gottesman and Lo. We propose a measurement-free reconstruction circuit of quantum secrets in quantum secret sharing based on stabilizer codes. Our reconstruction circuit has width\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$k+|J|$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mo>|<\/mml:mo>\n                            <mml:mi>J<\/mml:mi>\n                            <mml:mo>|<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and consists of\n                    <jats:italic>O<\/jats:italic>\n                    (\n                    <jats:italic>k<\/jats:italic>\n                    |\n                    <jats:italic>J<\/jats:italic>\n                    |) one- or two-qudit unitary gates when |\n                    <jats:italic>J<\/jats:italic>\n                    | participants reconstruct\n                    <jats:italic>k<\/jats:italic>\n                    -qudit quantum secrets.\n                  <\/jats:p>","DOI":"10.1007\/s11128-025-04943-y","type":"journal-article","created":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T18:17:28Z","timestamp":1759169848000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing"],"prefix":"10.1007","volume":"24","author":[{"given":"Shogo","family":"Chiwaki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5085-8879","authenticated-orcid":false,"given":"Ryutaroh","family":"Matsumoto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,9,29]]},"reference":[{"key":"4943_CR1","doi-asserted-by":"publisher","unstructured":"Aschbacher, M.: Finite Group Theory, 2nd edn. Cambridge Studies in Advanced Mathematics, vol. 10. Cambridge University Press, Cambridge (2000). https:\/\/doi.org\/10.1017\/CBO9781139175319","DOI":"10.1017\/CBO9781139175319"},{"issue":"7","key":"4943_CR2","doi-asserted-by":"publisher","first-page":"3065","DOI":"10.1109\/18.959288","volume":"47","author":"A Ashikhmin","year":"2001","unstructured":"Ashikhmin, A., Knill, E.: Nonbinary quantum stabilizer codes. IEEE Trans. Inf. Theory 47(7), 3065\u20133072 (2001). https:\/\/doi.org\/10.1109\/18.959288","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"4943_CR3","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1007\/s00778-017-0470-9","volume":"26","author":"V Attasena","year":"2017","unstructured":"Attasena, V., Darmont, J., Harbi, N.: Secret sharing for cloud data security: a survey. VLDB J. 26(5), 657\u2013681 (2017). https:\/\/doi.org\/10.1007\/s00778-017-0470-9","journal-title":"VLDB J."},{"key":"4943_CR4","doi-asserted-by":"publisher","first-page":"3217","DOI":"10.1103\/PhysRevLett.78.3217","volume":"78","author":"CH Bennett","year":"1997","unstructured":"Bennett, C.H., DiVincenzo, D.P., Smolin, J.A.: Capacities of quantum erasure channels. Phys. Rev. Lett. 78, 3217\u20133220 (1997). https:\/\/doi.org\/10.1103\/PhysRevLett.78.3217","journal-title":"Phys. Rev. Lett."},{"key":"4943_CR5","doi-asserted-by":"publisher","unstructured":"Blakley, G.R.: Safeguarding cryptographic keys. In: AFIPS International Workshop on Managing Requirements Knowledge, pp. 242\u2013269. IEEE, New York (1979). https:\/\/doi.org\/10.1109\/AFIPS.1979.98","DOI":"10.1109\/AFIPS.1979.98"},{"issue":"1","key":"4943_CR6","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1109\/MNET.001.1900092","volume":"34","author":"AS Cacciapuoti","year":"2020","unstructured":"Cacciapuoti, A.S., Caleffi, M., Tafuri, F., Cataliotti, F.S., Gherardini, S., Bianchi, G.: Quantum internet: networking challenges in distributed quantum computing. IEEE Network 34(1), 137\u2013143 (2020). https:\/\/doi.org\/10.1109\/MNET.001.1900092","journal-title":"IEEE Network"},{"issue":"3","key":"4943_CR7","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1103\/PhysRevLett.78.405","volume":"78","author":"AR Calderbank","year":"1997","unstructured":"Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction and orthogonal geometry. Phys. Rev. Lett. 78(3), 405\u2013408 (1997). https:\/\/doi.org\/10.1103\/PhysRevLett.78.405","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"4943_CR8","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1109\/18.681315","volume":"44","author":"AR Calderbank","year":"1998","unstructured":"Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over gf(4). IEEE Trans. Inf. Theory 44(4), 1369\u20131387 (1998). https:\/\/doi.org\/10.1109\/18.681315","journal-title":"IEEE Trans. Inf. Theory"},{"key":"4943_CR9","doi-asserted-by":"publisher","unstructured":"Chiwaki, S., Matsumoto, R.: Performance comparison of the two reconstruction methods for stabilizer-based quantum secret sharing. IEICE Trans. Fundam. E107-A(3), 526\u2013529 (2024) https:\/\/doi.org\/10.1587\/transfun.2023TAL0001","DOI":"10.1587\/transfun.2023TAL0001"},{"key":"4943_CR10","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1103\/PhysRevA.56.76","volume":"56","author":"R Cleve","year":"1997","unstructured":"Cleve, R., Gottesman, D.: Efficient computations of encodings for quantum error correction. Phys. Rev. A 56, 76\u201382 (1997). https:\/\/doi.org\/10.1103\/PhysRevA.56.76","journal-title":"Phys. Rev. A"},{"issue":"3","key":"4943_CR11","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1103\/PhysRevLett.83.648","volume":"83","author":"R Cleve","year":"1999","unstructured":"Cleve, R., Gottesman, D., Lo, H.-K.: How to share a quantum secret. Phys. Rev. Lett. 83(3), 648\u2013651 (1999). https:\/\/doi.org\/10.1103\/PhysRevLett.83.648","journal-title":"Phys. Rev. Lett."},{"key":"4943_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.033042","volume":"2","author":"N Delfosse","year":"2020","unstructured":"Delfosse, N., Z\u00e9mor, G.: Linear-time maximum likelihood decoding of surface codes over the quantum erasure channel. Phys. Rev. Res. 2, 033042 (2020). https:\/\/doi.org\/10.1103\/PhysRevResearch.2.033042","journal-title":"Phys. Rev. Res."},{"key":"4943_CR13","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1007\/s11128-019-2234-5","volume":"18","author":"C Galindo","year":"2019","unstructured":"Galindo, C.: Entanglement-assisted quantum error-correcting codes over arbitrary finite fields. Quantum Inf. Process 18, 116 (2019). https:\/\/doi.org\/10.1007\/s11128-019-2234-5","journal-title":"Quantum Inf. Process"},{"issue":"3","key":"4943_CR14","doi-asserted-by":"publisher","first-page":"1862","DOI":"10.1103\/PhysRevA.54.1862","volume":"54","author":"D Gottesman","year":"1996","unstructured":"Gottesman, D.: Class of quantum error-correcting codes saturating the quantum hamming bound. Phys. Rev. A 54(3), 1862\u20131868 (1996). https:\/\/doi.org\/10.1103\/PhysRevA.54.1862","journal-title":"Phys. Rev. A"},{"issue":"4","key":"4943_CR15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.61.042311","volume":"61","author":"D Gottesman","year":"2000","unstructured":"Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000). https:\/\/doi.org\/10.1103\/PhysRevA.61.042311","journal-title":"Phys. Rev. A"},{"key":"4943_CR16","doi-asserted-by":"publisher","unstructured":"Grassl, M.: Variations on encoding circuits for stabilizer quantum codes. In: Chee, Y.M., (eds.) IWCC 2011. Lecture Notes in Computer Science, vol. 6639, pp. 142\u2013158. Springer, New York (2011). https:\/\/doi.org\/10.1007\/978-3-642-20901-7_9","DOI":"10.1007\/978-3-642-20901-7_9"},{"key":"4943_CR17","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1103\/PhysRevA.56.33","volume":"56","author":"M Grassl","year":"1997","unstructured":"Grassl, M., Beth, T., Pellizzari, T.: Codes for the quantum erasure channel. Phys. Rev. A 56, 33\u201338 (1997). https:\/\/doi.org\/10.1103\/PhysRevA.56.33","journal-title":"Phys. Rev. A"},{"issue":"5","key":"4943_CR18","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1142\/S0129054103002011","volume":"14","author":"M Grassl","year":"2003","unstructured":"Grassl, M., R\u00f6tteler, M., Beth, T.: Efficient quantum circuits for non-qubit quantum error-correcting codes. Int. J. Found. Comput. Sci. 14(5), 757\u2013775 (2003). https:\/\/doi.org\/10.1142\/S0129054103002011","journal-title":"Int. J. Found. Comput. Sci."},{"key":"4943_CR19","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.5.010333","volume":"5","author":"S Heu\u00dfen","year":"2024","unstructured":"Heu\u00dfen, S., Locher, D.F., M\u00fcller, M.: Measurement-free fault-tolerant quantum error correction in near-term devices. PRX Quantum 5, 010333 (2024). https:\/\/doi.org\/10.1103\/PRXQuantum.5.010333","journal-title":"PRX Quantum"},{"key":"4943_CR20","doi-asserted-by":"publisher","first-page":"1829","DOI":"10.1103\/PhysRevA.59.1829","volume":"59","author":"M Hillery","year":"1999","unstructured":"Hillery, M., Bu\u017eek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829\u20131834 (1999). https:\/\/doi.org\/10.1103\/PhysRevA.59.1829","journal-title":"Phys. Rev. A"},{"key":"4943_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.comnet.2022.109092","volume":"213","author":"J Illiano","year":"2022","unstructured":"Illiano, J., Caleffi, M., Manzalini, A., Cacciapuoti, A.S.: Quantum internet protocol stack: a comprehensive survey. Computer Netw. 213, 109092 (2022). https:\/\/doi.org\/10.1016\/j.comnet.2022.109092","journal-title":"Computer Netw."},{"key":"4943_CR22","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.4.020358","volume":"4","author":"M Kang","year":"2023","unstructured":"Kang, M., Campbell, W.C., Brown, K.R.: Quantum error correction with metastable states of trapped ions using erasure conversion. PRX Quantum 4, 020358 (2023). https:\/\/doi.org\/10.1103\/PRXQuantum.4.020358","journal-title":"PRX Quantum"},{"key":"4943_CR23","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1103\/PhysRevA.59.162","volume":"59","author":"A Karlsson","year":"1999","unstructured":"Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162\u2013168 (1999). https:\/\/doi.org\/10.1103\/PhysRevA.59.162","journal-title":"Phys. Rev. A"},{"issue":"11","key":"4943_CR24","doi-asserted-by":"publisher","first-page":"4892","DOI":"10.1109\/TIT.2006.883612","volume":"52","author":"A Ketkar","year":"2006","unstructured":"Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbainary stabilizer codes over finite fields. IEEE Trans. Inform. Theory 52(11), 4892\u20134924 (2006). https:\/\/doi.org\/10.1109\/TIT.2006.883612","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"4","key":"4943_CR25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.88.042332","volume":"88","author":"A Marin","year":"2013","unstructured":"Marin, A., Markham, D.: Equivalence between sharing quantum and classical secrets and error correction. Phys. Rev. A 88(4), 042332 (2013). https:\/\/doi.org\/10.1103\/PhysRevA.88.042332","journal-title":"Phys. Rev. A"},{"issue":"4","key":"4943_CR26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.78.042309","volume":"78","author":"D Markham","year":"2008","unstructured":"Markham, D., Sanders, B.C.: Graph states for quantum secret sharing. Phys. Rev. A 78(4), 042309 (2008). https:\/\/doi.org\/10.1103\/PhysRevA.78.042309","journal-title":"Phys. Rev. A"},{"issue":"8","key":"4943_CR27","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1007\/s11128-017-1656-1","volume":"16","author":"R Matsumoto","year":"2017","unstructured":"Matsumoto, R.: Unitary reconstruction of secret for stabilizer based quantum secret sharing. Quant. Inf. Process. 16(8), 202 (2017). https:\/\/doi.org\/10.1007\/s11128-017-1656-1","journal-title":"Quant. Inf. Process."},{"key":"4943_CR28","doi-asserted-by":"publisher","first-page":"2100107","DOI":"10.1109\/TQE.2025.3530939","volume":"6","author":"R Matsumoto","year":"2025","unstructured":"Matsumoto, R.: Advance sharing procedures for the ramp quantum secret sharing schemes with the highest coding rate. IEEE Trans. Quantum Eng. 6, 2100107 (2025). https:\/\/doi.org\/10.1109\/TQE.2025.3530939","journal-title":"IEEE Trans. Quantum Eng."},{"issue":"3","key":"4943_CR29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.72.032318","volume":"72","author":"T Ogawa","year":"2005","unstructured":"Ogawa, T., Sasaki, A., Iwamoto, M., Yamamoto, H.: Quantum secret sharing schemes and reversibility of quantum operations. Phys. Rev. A 72(3), 032318 (2005). https:\/\/doi.org\/10.1103\/PhysRevA.72.032318","journal-title":"Phys. Rev. A"},{"key":"4943_CR30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.108.062426","volume":"108","author":"MA Perlin","year":"2023","unstructured":"Perlin, M.A., Premakumar, V.N., Wang, J., Saffman, M., Joynt, R.: Fault-tolerant measurement-free quantum error correction with multiqubit gates. Phys. Rev. A 108, 062426 (2023). https:\/\/doi.org\/10.1103\/PhysRevA.108.062426","journal-title":"Phys. Rev. A"},{"issue":"4","key":"4943_CR31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.86.042303","volume":"86","author":"PK Sarvepalli","year":"2012","unstructured":"Sarvepalli, P.K.: Nonthreshold quantum secret-sharing schemes in the graph-state formalism. Phys. Rev. A 86(4), 042303 (2012). https:\/\/doi.org\/10.1103\/PhysRevA.86.042303","journal-title":"Phys. Rev. A"},{"key":"4943_CR32","first-page":"142","volume":"2","author":"P Sarvepalli","year":"2009","unstructured":"Sarvepalli, P., Klappenecker, A.: Encoding subsystem codes. Int. J. Adv. Secur. 2, 142\u2013155 (2009)","journal-title":"Int. J. Adv. Secur."},{"issue":"11","key":"4943_CR33","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1145\/359168.359176","volume":"22","author":"A Shamir","year":"1979","unstructured":"Shamir, A.: How to share a secret. Commun. ACM 22(11), 612\u2013613 (1979). https:\/\/doi.org\/10.1145\/359168.359176","journal-title":"Commun. ACM"},{"key":"4943_CR34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.6.043253","volume":"6","author":"S Veroni","year":"2024","unstructured":"Veroni, S., M\u00fcller, M., Giudice, G.: Optimized measurement-free and fault-tolerant quantum error correction for neutral atoms. Phys. Rev. Res. 6, 043253 (2024). https:\/\/doi.org\/10.1103\/PhysRevResearch.6.043253","journal-title":"Phys. Rev. Res."},{"key":"4943_CR35","doi-asserted-by":"publisher","first-page":"4657","DOI":"10.1038\/s41467-022-32094-6","volume":"13","author":"Y Wu","year":"2022","unstructured":"Wu, Y., Kolkowitz, S., Puri, S., Thompson, J.D.: Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays. Nat. Commun. 13, 4657 (2022). https:\/\/doi.org\/10.1038\/s41467-022-32094-6","journal-title":"Nat. Commun."},{"key":"4943_CR36","doi-asserted-by":"publisher","unstructured":"Zhang, P., Matsumoto, R.: Quantum strongly secure ramp secret sharing. Quantum Inf. Process. 14(2), 715\u2013729 (2015). https:\/\/doi.org\/10.1007\/s11128-014-0863-2","DOI":"10.1007\/s11128-014-0863-2"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04943-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-04943-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04943-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T09:46:55Z","timestamp":1761817615000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-04943-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,29]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["4943"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-04943-y","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2025,9,29]]},"assertion":[{"value":"31 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 September 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"322"}}