{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T13:55:58Z","timestamp":1754488558214,"version":"3.37.3"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:00:00Z","timestamp":1614556800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:00:00Z","timestamp":1614556800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s11128-020-02976-z","type":"journal-article","created":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T06:02:45Z","timestamp":1614924165000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Mermin polynomials for non-locality and entanglement detection in Grover\u2019s algorithm and Quantum Fourier Transform"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2571-0506","authenticated-orcid":false,"given":"Henri","family":"de Boutray","sequence":"first","affiliation":[]},{"given":"Hamza","family":"Jaffali","sequence":"additional","affiliation":[]},{"given":"Fr\u00e9d\u00e9ric","family":"Holweck","sequence":"additional","affiliation":[]},{"given":"Alain","family":"Giorgetti","sequence":"additional","affiliation":[]},{"given":"Pierre-Alain","family":"Masson","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,5]]},"reference":[{"issue":"3","key":"2976_CR1","doi-asserted-by":"publisher","first-page":"032102","DOI":"10.1103\/PhysRevA.94.032102","volume":"94","author":"D Alsina","year":"2016","unstructured":"Alsina, D., Cervera, A., Goyeneche, D., Latorre, J.I., \u017byczkowski, K.: Operational approach to Bell inequalities: application to qutrits. Phys. Rev. A 94(3), 032102 (2016)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"2976_CR2","doi-asserted-by":"publisher","first-page":"012314","DOI":"10.1103\/PhysRevA.94.012314","volume":"94","author":"D Alsina","year":"2016","unstructured":"Alsina, D., Latorre, J.I.: Experimental test of Mermin inequalities on a 5-qubit quantum computer. Phys. Rev. A 94(1), 012314 (2016)","journal-title":"Phys. Rev. A"},{"key":"2976_CR3","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1088\/1367-2630\/7\/1\/088","volume":"7","author":"N Brunner","year":"2005","unstructured":"Brunner, N., Gisin, N., Scarani, V.: Entanglement and non-locality are different resources. New J. Phys. 7, 88 (2005)","journal-title":"New J. Phys."},{"issue":"6","key":"2976_CR4","doi-asserted-by":"publisher","first-page":"062312","DOI":"10.1103\/PhysRevA.65.062312","volume":"65","author":"O Biham","year":"2002","unstructured":"Biham, O., Nielsen, M.A., Osborne, T.J.: Entanglement monotone derived from Grover\u2019s algorithm. Phys. Rev. A 65(6), 062312 (2002)","journal-title":"Phys. Rev. A"},{"issue":"2","key":"2976_CR5","doi-asserted-by":"publisher","first-page":"833","DOI":"10.1007\/s11128-015-1174-y","volume":"15","author":"J Batle","year":"2016","unstructured":"Batle, J., Ooi, C.H.R., Farouk, A., Alkhambashi, M.S., Abdalla, S.: Global versus local quantum correlations in the Grover search algorithm. Quantum Inf. Process. 15(2), 833\u2013849 (2016)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"2976_CR6","first-page":"399","volume":"2","author":"SL Braunstein","year":"2002","unstructured":"Braunstein, S.L., Pati, A.K.: Speed-up and entanglement in quantum searching. Quantum Inf. Comput. 2(5), 399\u2013409 (2002)","journal-title":"Quantum Inf. Comput."},{"key":"2976_CR7","unstructured":"Chakraborty, S., Banerjee, S., Adhikari, S., Kumar, A.: Entanglement in the Grover\u2019s search algorithm. arXiv:1305.4454 [quant-ph] (2013)"},{"issue":"17","key":"2976_CR8","doi-asserted-by":"publisher","first-page":"170405","DOI":"10.1103\/PhysRevLett.88.170405","volume":"88","author":"D Collins","year":"2002","unstructured":"Collins, D., Gisin, N., Popescu, S., Roberts, D., Scarani, V.: Bell-type inequalities to detect true n-body non-separability. Phys. Rev. Lett. 88(17), 170405 (2002)","journal-title":"Phys. Rev. Lett."},{"issue":"15","key":"2976_CR9","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1103\/PhysRevLett.23.880","volume":"23","author":"JF Clauser","year":"1969","unstructured":"Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23(15), 880\u2013884 (1969)","journal-title":"Phys. Rev. Lett."},{"key":"2976_CR10","doi-asserted-by":"publisher","first-page":"1769","DOI":"10.1098\/rsta.1998.0248","volume":"356","author":"A Ekert","year":"1998","unstructured":"Ekert, A., Jozsa, R.: Quantum algorithms: entanglement-enhanced information processing. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 356, 1769\u20131782 (1998)","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"key":"2976_CR11","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, STOC \u201996. New York, NY, USA. ACM, pp. 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"issue":"1","key":"2976_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2009.02.004","volume":"474","author":"O G\u00fchne","year":"2009","unstructured":"G\u00fchne, O., T\u00f3th, G.: Entanglement detection. Phys. Rep. 474(1), 1\u201375 (2009)","journal-title":"Phys. Rep."},{"key":"2976_CR13","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/978-1-4939-1590-3_9","volume-title":"Symmetry: Representation Theory and Its Applications. Honor of Nolan R. Wallach, Progress in Mathematics","author":"G Gour","year":"2014","unstructured":"Gour, G., Wallach, N.R.: On symmetric SL-invariant polynomials in four qubits. In: Howe, R., Hunziker, M., Willenbring, J.F. (eds.) Symmetry: Representation Theory and Its Applications. Honor of Nolan R. Wallach, Progress in Mathematics, pp. 259\u2013267. Springer, New York, NY (2014)"},{"issue":"11","key":"2976_CR14","doi-asserted-by":"publisher","first-page":"4391","DOI":"10.1007\/s11128-016-1445-2","volume":"15","author":"F Holweck","year":"2016","unstructured":"Holweck, F., Jaffali, H., Nounouh, I.: Grover\u2019s algorithm and the secant varieties. Quantum Inf. Process. 15(11), 4391\u20134413 (2016)","journal-title":"Quantum Inf. Process."},{"issue":"10","key":"2976_CR15","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1145\/363235.363259","volume":"12","author":"CAR Hoare","year":"1969","unstructured":"Hoare, C.A.R.: An axiomatic basis for computer programming. Commun. ACM 12(10), 576\u2013580 (1969)","journal-title":"Commun. ACM"},{"issue":"4","key":"2976_CR16","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/S0375-9601(00)00480-1","volume":"273","author":"A Higuchi","year":"2000","unstructured":"Higuchi, A., Sudbery, A.: How entangled can two couples get? Phys. Lett. A 273(4), 213\u2013217 (2000)","journal-title":"Phys. Lett. A"},{"issue":"5","key":"2976_CR17","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s11128-019-2249-y","volume":"18","author":"H Jaffali","year":"2019","unstructured":"Jaffali, H., Holweck, F.: Quantum Entanglement involved in Grover\u2019s and Shor\u2019s algorithms: the four-qubit case. Quantum Inf. Process. 18(5), 133 (2019)","journal-title":"Quantum Inf. Process."},{"issue":"2036","key":"2976_CR18","doi-asserted-by":"publisher","first-page":"2011","DOI":"10.1098\/rspa.2002.1097","volume":"459","author":"R Jozsa","year":"2003","unstructured":"Jozsa, R., Linden, N.: On the role of entanglement in quantum computational speed-up. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 459(2036), 2011\u20132032 (2003)","journal-title":"Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"issue":"7","key":"2976_CR19","first-page":"630","volume":"6","author":"VM Kendon","year":"2006","unstructured":"Kendon, V.M., Munro, W.J.: Entanglement and its role in Shor\u2019s algorithm. Quantum Inf. Comput. 6(7), 630\u2013640 (2006)","journal-title":"Quantum Inf. Comput."},{"key":"2976_CR20","unstructured":"Lavor, C., Manssur, L.R.U., Portugal, R.: Grover\u2019s Algorithm: Quantum Database Search. arXiv:quant-ph\/0301079 (2003)"},{"issue":"4","key":"2976_CR21","doi-asserted-by":"publisher","first-page":"042303","DOI":"10.1103\/PhysRevA.67.042303","volume":"67","author":"J-G Luque","year":"2003","unstructured":"Luque, J.-G., Thibon, J.-Y.: The polynomial invariants of four qubits. Phys. Rev. A 67(4), 042303 (2003)","journal-title":"Phys. Rev. A"},{"issue":"15","key":"2976_CR22","doi-asserted-by":"publisher","first-page":"1838","DOI":"10.1103\/PhysRevLett.65.1838","volume":"65","author":"ND Mermin","year":"1990","unstructured":"Mermin, N.D.: Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65(15), 1838\u20131840 (1990)","journal-title":"Phys. Rev. Lett."},{"issue":"9","key":"2976_CR23","doi-asserted-by":"publisher","first-page":"4273","DOI":"10.1063\/1.1497700","volume":"43","author":"DA Meyer","year":"2002","unstructured":"Meyer, D.A., Wallach, N.R.: Global entanglement in multiparticle systems. J. Math. Phys. 43(9), 4273\u20134278 (2002)","journal-title":"J. Math. Phys."},{"issue":"7","key":"2976_CR24","first-page":"540","volume":"2","author":"A Miyake","year":"2002","unstructured":"Miyake, A., Wadati, M.: Multipartite entanglement and hyperdeterminants. Quantum Inf. Comput. 2(7), 540\u2013555 (2002)","journal-title":"Quantum Inf. Comput."},{"key":"2976_CR25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511976667","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 edn. Cambridge University Press, Cambridge (2010)","edition":"Anniversary"},{"issue":"03","key":"2976_CR26","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1142\/S0219749906001980","volume":"04","author":"A Osterloh","year":"2006","unstructured":"Osterloh, A., Siewert, J.: Entanglement monotones and maximally entangled states in multipartite qubit systems. Int. J. Quantum Inf. 04(03), 531\u2013540 (2006)","journal-title":"Int. J. Quantum Inf."},{"issue":"2","key":"2976_CR27","first-page":"1","volume":"87","author":"M Rossi","year":"2013","unstructured":"Rossi, M., Bru\u00df, D., Macchiavello, C.: Scale invariance of entanglement dynamics in Grover\u2019s quantum search algorithm. Phys. Rev. A Atom. Mol. Opt. Phys. 87(2), 1\u20135 (2013)","journal-title":"Phys. Rev. A Atom. Mol. Opt. Phys."},{"issue":"1","key":"2976_CR28","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1111\/j.1749-6632.1995.tb39008.x","volume":"755","author":"A Shimony","year":"1995","unstructured":"Shimony, A.: Degree of entanglement. Ann. N. Y. Acad. Sci. 755(1), 675\u2013679 (1995)","journal-title":"Ann. N. Y. Acad. Sci."},{"key":"2976_CR29","unstructured":"Shor, P.W., Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science. Santa Fe, NM, USA, : IEEE Comput. Press, Soc, pp. 124\u2013134 (1994)"},{"issue":"6","key":"2976_CR30","doi-asserted-by":"publisher","first-page":"062308","DOI":"10.1103\/PhysRevA.72.062308","volume":"72","author":"Y Shimoni","year":"2005","unstructured":"Shimoni, Y., Shapira, D., Biham, O.: Entangled quantum states generated by Shor\u2019s factoring algorithm. Phys. Rev. A 72(6), 062308 (2005)","journal-title":"Phys. Rev. A"},{"issue":"2","key":"2976_CR31","doi-asserted-by":"publisher","first-page":"022340","DOI":"10.1103\/PhysRevA.72.022340","volume":"72","author":"G Toth","year":"2005","unstructured":"Toth, G., Guehne, O.: Entanglement detection in the stabilizer formalism. Phys. Rev. A 72(2), 022340 (2005)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"2976_CR32","doi-asserted-by":"publisher","first-page":"052112","DOI":"10.1103\/PhysRevA.65.052112","volume":"65","author":"F Verstraete","year":"2002","unstructured":"Verstraete, F., Dehaene, J., De Moor, B., Verschelde, H.: Four qubits can be entangled in nine different ways. Phys. Rev. A 65(5), 052112 (2002)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"2976_CR33","doi-asserted-by":"publisher","first-page":"042307","DOI":"10.1103\/PhysRevA.68.042307","volume":"68","author":"T-C Wei","year":"2003","unstructured":"Wei, T.-C., Goldbart, P.M.: Geometric measure of entanglement and applications to bipartite and multipartite quantum states. Phys. Rev. A 68(4), 042307 (2003)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"2976_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2049706.2049708","volume":"33","author":"M Ying","year":"2011","unstructured":"Ying, M.: Floyd\u2013Hoare logic for quantum programs. ACM Trans. Program. Lang. Syst. 33(6), 1\u201349 (2011)","journal-title":"ACM Trans. Program. Lang. Syst."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02976-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-020-02976-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02976-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T23:05:43Z","timestamp":1617231943000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-020-02976-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["2976"],"URL":"https:\/\/doi.org\/10.1007\/s11128-020-02976-z","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"type":"print","value":"1570-0755"},{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2021,3]]},"assertion":[{"value":"16 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 December 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"91"}}