{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:27:15Z","timestamp":1740137235342,"version":"3.37.3"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T00:00:00Z","timestamp":1721001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T00:00:00Z","timestamp":1721001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004901","name":"Funda\u00e7\u00e3o de Amparo \u00e1 Pesquisa do Estado de Minas Gerais","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004901","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-024-04480-0","type":"journal-article","created":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T07:02:02Z","timestamp":1721026922000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Unexpected averages of mixing matrices"],"prefix":"10.1007","volume":"23","author":[{"given":"Pedro","family":"Baptista","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1581-431X","authenticated-orcid":false,"given":"Gabriel","family":"Coutinho","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vitor","family":"Marques","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,15]]},"reference":[{"key":"4480_CR1","doi-asserted-by":"crossref","unstructured":"Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.: Quantum walks on graphs. In Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pp. 50\u201359 (2001)","DOI":"10.1145\/380752.380758"},{"key":"4480_CR2","doi-asserted-by":"crossref","unstructured":"Moore, C., Russell, A.: Quantum walks on the hypercube. In: International Workshop on Randomization and Approximation Techniques in Computer Science, pp. 164\u2013178. Springer (2002)","DOI":"10.1007\/3-540-45726-7_14"},{"key":"4480_CR3","unstructured":"Adamczak, W., Andrew, K., Hernberg, P., Tamon, C.: A note on graphs resistant to quantum uniform mixing (2003). arXiv preprint arXiv:quant-ph\/0308073"},{"issue":"06","key":"4480_CR4","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1142\/S0219749907003195","volume":"5","author":"W Adamczak","year":"2007","unstructured":"Adamczak, W., Andrew, K., Bergen, L., Ethier, D., Hernberg, P., Lin, J., Tamon, C.: Non-uniform mixing of quantum walk on cycles. Int. J. Quant. Inf. 5(06), 781\u2013793 (2007)","journal-title":"Int. J. Quant. Inf."},{"issue":"1","key":"4480_CR5","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.disc.2011.06.032","volume":"312","author":"CD Godsil","year":"2012","unstructured":"Godsil, C.D.: State transfer on graphs. Discret. Math. 312(1), 129\u2013147 (2012)","journal-title":"Discret. Math."},{"issue":"7","key":"4480_CR6","doi-asserted-by":"publisher","first-page":"1649","DOI":"10.1016\/j.jcta.2013.05.006","volume":"120","author":"C Godsil","year":"2013","unstructured":"Godsil, C.: Average mixing of continuous quantum walks. J. Comb. Theory Ser. A 120(7), 1649\u20131662 (2013)","journal-title":"J. Comb. Theory Ser. A"},{"issue":"4","key":"4480_CR7","first-page":"4","volume":"25","author":"G Coutinho","year":"2018","unstructured":"Coutinho, G., Godsil, C., Guo, K., Zhan, H.: A New Perspective on the Average Mixing Matrix. Electron. J. Comb. 25(4), 4\u201314 (2018)","journal-title":"Electron. J. Comb."},{"key":"4480_CR8","doi-asserted-by":"publisher","first-page":"269","DOI":"10.13001\/1081-3810.3746","volume":"34","author":"C Godsil","year":"2018","unstructured":"Godsil, C., Guo, K., Sinkovic, J.: Average mixing matrix of trees. Electron. J. Linear Algebra 34, 269\u2013282 (2018)","journal-title":"Electron. J. Linear Algebra"},{"key":"4480_CR9","unstructured":"Godsil, C., Guo, K., Sobchuk, M.: Diagonal entries of the average mixing matrix (2019). arXiv preprint arXiv:1910.02039"},{"key":"4480_CR10","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1016\/j.laa.2020.08.027","volume":"614","author":"C Godsil","year":"2021","unstructured":"Godsil, C.: Sedentary quantum walks. Linear Algebra Appl. 614, 356\u2013375 (2021)","journal-title":"Linear Algebra Appl."},{"key":"4480_CR11","unstructured":"Schervish, M.J., DeGroot, M.H.: Probability and Statistics, Volume 563. Pearson Education London, UK (2014)"},{"key":"4480_CR12","doi-asserted-by":"crossref","unstructured":"Strichartz, R.S.: A Guide to Distribution Theory and Fourier Transforms. World Scientific Publishing Company (2003)","DOI":"10.1142\/5314"},{"key":"4480_CR13","doi-asserted-by":"crossref","unstructured":"Horn,R.A., Johnson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press (2012)","DOI":"10.1017\/CBO9781139020411"},{"key":"4480_CR14","unstructured":"Coutinho, G., Godsil, C.: Continuous-time quantum walks in graphs. IMAGE\u2014The Bulletin of the International Linear Algebra Society, Spring:12\u201321 (2018)"},{"issue":"3","key":"4480_CR15","doi-asserted-by":"publisher","first-page":"3","DOI":"10.37236\/6855","volume":"24","author":"C Godsil","year":"2017","unstructured":"Godsil, C., Zhan, H.: Uniform Mixing on Cayley Graphs. Electron. J. Combin. 24(3), 3\u201320 (2017)","journal-title":"Electron. J. Combin."},{"key":"4480_CR16","unstructured":"Feller, W.: An Introduction to Probability Theory and Its Applications, Volume 2, volume\u00a081. Wiley (1991)"},{"key":"4480_CR17","doi-asserted-by":"crossref","unstructured":"Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Universitext. Springer, New York (2012)","DOI":"10.1007\/978-1-4614-1939-6"},{"issue":"3","key":"4480_CR18","doi-asserted-by":"publisher","first-page":"32312","DOI":"10.1103\/PhysRevA.71.032312","volume":"71","author":"M Christandl","year":"2005","unstructured":"Christandl, M., Datta, N., Dorlas, T.C., Ekert, A., Kay, A., Landahl, A.J.: Perfect transfer of arbitrary states in quantum spin networks. Phys. Rev. A 71(3), 32312 (2005)","journal-title":"Phys. Rev. A"},{"key":"4480_CR19","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/0024-3795(75)90075-0","volume":"10","author":"Man Duen Choi","year":"1975","unstructured":"Man Duen Choi: Completely positive linear maps on complex matrices. Linear Algebra Appl. 10, 285\u2013290 (1975)","journal-title":"Linear Algebra Appl."},{"key":"4480_CR20","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/0024-3795(93)90274-R","volume":"193","author":"LJ Landau","year":"1993","unstructured":"Landau, L.J., Streater, R.F.: On Birkhoff\u2019s theorem for doubly stochastic completely positive maps of matrix algebras. Linear Algebra Appl. 193, 107\u2013127 (1993)","journal-title":"Linear Algebra Appl."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04480-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-024-04480-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04480-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T17:41:06Z","timestamp":1722361266000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-024-04480-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,15]]},"references-count":20,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["4480"],"URL":"https:\/\/doi.org\/10.1007\/s11128-024-04480-0","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2024,7,15]]},"assertion":[{"value":"30 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 July 2024","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 have no other relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"272"}}