{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:27:37Z","timestamp":1740137257493,"version":"3.37.3"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,4,8]],"date-time":"2023-04-08T00:00:00Z","timestamp":1680912000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,4,8]],"date-time":"2023-04-08T00:00:00Z","timestamp":1680912000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["Grant No. ZG216S2005"],"award-info":[{"award-number":["Grant No. ZG216S2005"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-023-03913-6","type":"journal-article","created":{"date-parts":[[2023,4,8]],"date-time":"2023-04-08T19:02:37Z","timestamp":1680980557000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Zero entries distribution in a unitary matrix"],"prefix":"10.1007","volume":"22","author":[{"given":"Shaomin","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1544-8874","authenticated-orcid":false,"given":"Changchun","family":"Feng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,4,8]]},"reference":[{"key":"3913_CR1","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/j.laa.2016.10.028","volume":"514","author":"S De Baerdemacker","year":"2017","unstructured":"De Baerdemacker, S., De Vos, A., Chen, L., Li, Yu.: The Birkhoff theorem of unitary matrices of arbitrary dimensions. Linear Algebra Appl. 514, 151\u2013164 (2017)","journal-title":"Linear Algebra Appl."},{"key":"3913_CR2","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1016\/j.laa.2018.07.018","volume":"557","author":"A Muller-Hermes","year":"2018","unstructured":"Muller-Hermes, A., Nechita, I.: Operator Schmidt ranks of bipartite unitary matrices. Linear Algebra Appl. 557, 174\u2013187 (2018)","journal-title":"Linear Algebra Appl."},{"key":"3913_CR3","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.laa.2020.01.020","volume":"592","author":"Y Ouyang","year":"2020","unstructured":"Ouyang, Y., Shen, Y., Chen, L.: Faster quantum computation with permutations and resonant couplings. Linear Algebra Appl. 592, 270\u2013286 (2020)","journal-title":"Linear Algebra Appl."},{"key":"3913_CR4","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2000","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)"},{"key":"3913_CR5","volume-title":"Giuliano Strini","author":"G Benenti","year":"2004","unstructured":"Benenti, G., Casati, G.: Giuliano Strini. World Scientific, Principles of Quantum Computation and Information (2004)"},{"key":"3913_CR6","doi-asserted-by":"publisher","first-page":"190502","DOI":"10.1103\/PhysRevLett.110.190502","volume":"110","author":"V Kliuchnikov","year":"2013","unstructured":"Kliuchnikov, V., Maslov, D., Mosca, M.: Asymptotically optimal approximation of single qubit Unitaries by Clifford and t-circuits using a constant number of ancillary qubits. Phys. Rev. Lett. 110, 190502 (2013)","journal-title":"Phys. Rev. Lett."},{"key":"3913_CR7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.89.032301","volume":"89","author":"VS Malinovsky","year":"2014","unstructured":"Malinovsky, V.S., Sola, I.R., Vala, J.: Phase-controlled two-qubit quantum gates. Phys. Rev. A 89, 032301 (2014)","journal-title":"Phys. Rev. A"},{"key":"3913_CR8","doi-asserted-by":"publisher","first-page":"1895","DOI":"10.1103\/PhysRevLett.70.1895","volume":"70","author":"CH Bennett","year":"1993","unstructured":"Bennett, C.H., Brassard, G., Cr\u00e9peau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein\u2013Podolsk\u2013Rosen channels. Phys. Rev. Lett. 70, 1895\u20131899 (1993)","journal-title":"Phys. Rev. Lett."},{"issue":"15","key":"3913_CR9","first-page":"1","volume":"69","author":"M Liang","year":"2019","unstructured":"Liang, M., Mengyao, H., Sun, Y., Chen, L., Chen, X.: Real entries of complex Hadamard matrices and mutually unbiased bases in dimension six. Linear and Multilinear Algebra 69(15), 1\u201318 (2019)","journal-title":"Linear and Multilinear Algebra"},{"issue":"5","key":"3913_CR10","doi-asserted-by":"publisher","first-page":"1219","DOI":"10.1016\/j.ejc.2007.06.009","volume":"29","author":"F Sz\u00f6ll\u0151si","year":"2008","unstructured":"Sz\u00f6ll\u0151si, F.: Parametrizing complex Hadamard matrices. Eur. J. Combinat. 29(5), 1219\u20131234 (2008)","journal-title":"Eur. J. Combinat."},{"key":"3913_CR11","doi-asserted-by":"publisher","first-page":"7081","DOI":"10.1088\/0305-4470\/34\/35\/332","volume":"34","author":"RF Werner","year":"2001","unstructured":"Werner, R.F.: All teleportation and dense coding schemes. J. Phys. A 34, 7081\u20137094 (2001)","journal-title":"J. Phys. A"},{"key":"3913_CR12","doi-asserted-by":"publisher","first-page":"062326","DOI":"10.1103\/PhysRevA.89.062326","volume":"89","author":"L Chen","year":"2014","unstructured":"Chen, L., Li, Y.: Nonlocal and controlled unitary operators of Schmidt rank three. Phys. Rev. A 89, 062326 (2014)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"3913_CR13","first-page":"666","volume":"69","author":"V Shende","year":"2003","unstructured":"Shende, V., Markov, I., Bullock, S.: Minimal universal two-qubit controlled-not-based circuits. Phys. Rev. A 69(6), 666\u2013670 (2003)","journal-title":"Phys. Rev. A"},{"issue":"2","key":"3913_CR14","doi-asserted-by":"publisher","first-page":"910","DOI":"10.1103\/PhysRevA.60.910","volume":"60","author":"J Kempe","year":"1999","unstructured":"Kempe, J.: Multiparticle entanglement and its applications to crytography. Phys. Rev. A 60(2), 910\u2013916 (1999)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"3913_CR15","doi-asserted-by":"publisher","first-page":"052301","DOI":"10.1103\/PhysRevA.67.052301","volume":"67","author":"MA Nielsen","year":"2003","unstructured":"Nielsen, M.A., Dawson, C.M., Dodd, J.L., Gilchrist, A., Mortimer, D., Osborne, T.J., Bremner, M.J., Harrow, A.W., Hines, A.: Quantum dynamics as a physical resource. Phys. Rev. A 67(5), 052301 (2003)","journal-title":"Phys. Rev. A"},{"key":"3913_CR16","doi-asserted-by":"publisher","first-page":"062311","DOI":"10.1103\/PhysRevA.69.062311","volume":"69","author":"M Hein","year":"2004","unstructured":"Hein, M., Eisert, J., Briegel, H.J.: Multiparty entanglement in graph states. Phys. Rev. A 69, 062311 (2004)","journal-title":"Phys. Rev. A"},{"key":"3913_CR17","doi-asserted-by":"publisher","first-page":"943","DOI":"10.1038\/nphys1781","volume":"6","author":"JT Barreiro","year":"2010","unstructured":"Barreiro, J.T., Schindler, P., G\u00fchne, O., Monz, T., Chwalla, M., Roos, C.F., Hennrich, M., Blatt, R.: Experimental multiparticle entanglement dynamics induced by decoherence. Nat. Phys. 6, 943\u2013946 (2010)","journal-title":"Nat. Phys."},{"key":"3913_CR18","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1007\/s11128-021-03146-5","volume":"20","author":"C Feng","year":"2021","unstructured":"Feng, C., Chen, L.: Zero entries in multipartite product unitary matrices. Q. Inf. Process. 20, 250 (2021)","journal-title":"Q. Inf. Process."},{"issue":"7","key":"3913_CR19","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1038\/nphoton.2013.102","volume":"7","author":"M Tillmann","year":"2013","unstructured":"Tillmann, M., Dakic, B., Heilmann, R., Nolte, S., Szameit, A., Walther, P.: Experimental boson sampling. Nat. Photonics 7(7), 540\u2013544 (2013)","journal-title":"Nat. Photonics"},{"issue":"1","key":"3913_CR20","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1103\/PhysRevLett.73.58","volume":"73","author":"M Reck","year":"1994","unstructured":"Reck, M., Zeilinger, A., Bernstein, H., Bertani, P.: Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73(1), 58\u201361 (1994)","journal-title":"Phys. Rev. Lett."},{"issue":"01","key":"3913_CR21","doi-asserted-by":"publisher","first-page":"1350015","DOI":"10.1142\/S0219749913500159","volume":"11","author":"C-K Li","year":"2013","unstructured":"Li, C.-K., Roberts, R., Yin, X.: Decomposition of unitary matrices and quantum gates. Int. J. Q. Inf. 11(01), 1350015 (2013)","journal-title":"Int. J. Q. Inf."},{"issue":"7","key":"3913_CR22","first-page":"1","volume":"70","author":"ZW Song","year":"2020","unstructured":"Song, Z.W., Chen, L.: On the zero entries in a unitary matrix. Linear Multilinear Algebra 70(7), 1\u201310 (2020)","journal-title":"Linear Multilinear Algebra"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-023-03913-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-023-03913-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-023-03913-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T16:02:26Z","timestamp":1683216146000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-023-03913-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,8]]},"references-count":22,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["3913"],"URL":"https:\/\/doi.org\/10.1007\/s11128-023-03913-6","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2023,4,8]]},"assertion":[{"value":"5 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2023","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 that they have no conflict of interest to this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"169"}}