{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T15:51:12Z","timestamp":1778255472830,"version":"3.51.4"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T00:00:00Z","timestamp":1645142400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T00:00:00Z","timestamp":1645142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100009392","name":"Prince Sattam bin Abdulaziz University","doi-asserted-by":"publisher","award":["2020\/01\/12173"],"award-info":[{"award-number":["2020\/01\/12173"]}],"id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2022,3]]},"DOI":"10.1007\/s11128-022-03435-7","type":"journal-article","created":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T10:03:45Z","timestamp":1645178625000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Probability amplitude-encoded multichannel representation for quantum audio signals"],"prefix":"10.1007","volume":"21","author":[{"given":"Fei","family":"Yan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Song","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4964-6609","authenticated-orcid":false,"given":"Abdullah M.","family":"Iliyasu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kehan","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,2,18]]},"reference":[{"key":"3435_CR1","unstructured":"Cobos, M.: https:\/\/signalprocessingsociety.org\/publications-resources\/blog\/signal-processing-multimedia-world-how-science-behind-our-digital-life, Accessed on August 15th, (2020)"},{"issue":"6","key":"3435_CR2","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1109\/MSP.2002.1043298","volume":"19","author":"Y Eldar","year":"2002","unstructured":"Eldar, Y., Oppenheim, A.: Quantum signal processing. IEEE Sig. Process. Mag. 19(6), 12\u201332 (2002)","journal-title":"IEEE Sig. Process. Mag."},{"key":"3435_CR3","volume-title":"Quantum Computation and Quantum Information","author":"M Nielsen","year":"2000","unstructured":"Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)"},{"issue":"8","key":"3435_CR4","doi-asserted-by":"publisher","first-page":"2874","DOI":"10.3390\/e15082874","volume":"15","author":"A Iliyasu","year":"2013","unstructured":"Iliyasu, A.: Towards realising secure and efficient image and video processing applications on quantum computers. Entropy 15(8), 2874\u20132974 (2013)","journal-title":"Entropy"},{"key":"3435_CR5","doi-asserted-by":"publisher","first-page":"467C","DOI":"10.1007\/BF02650179","volume":"21","author":"R Feynman","year":"1982","unstructured":"Feynman, R.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467C \u2013 488 (1982)","journal-title":"Int. J. Theor. Phys."},{"key":"3435_CR6","doi-asserted-by":"crossref","unstructured":"Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. In: Proceedings of the Royal Society of London, 553\u2013558 (1992)","DOI":"10.1098\/rspa.1992.0167"},{"key":"3435_CR7","unstructured":"Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th annual symposium on foundations of computer science, 124\u2013134 (1994)"},{"key":"3435_CR8","doi-asserted-by":"crossref","unstructured":"Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM symposium on theory of computing, 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"key":"3435_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-015-1195-6","volume":"15","author":"F Yan","year":"2016","unstructured":"Yan, F., Iliyasu, A., Venegas-Andraca, S.: A survey of quantum image representations. Quan. Inf. Process. 15, 1\u201335 (2016)","journal-title":"Quan. Inf. Process."},{"issue":"1","key":"3435_CR10","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s11128-010-0177-y","volume":"10","author":"P Le","year":"2011","unstructured":"Le, P., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression and processing operations. Quan. Inf. Process. 10(1), 63\u201384 (2011)","journal-title":"Quan. Inf. Process."},{"key":"3435_CR11","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.ins.2011.09.028","volume":"186","author":"A Iliyasu","year":"2012","unstructured":"Iliyasu, A., Le, P., Dong, F., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186, 126\u2013149 (2012)","journal-title":"Inf. Sci."},{"key":"3435_CR12","doi-asserted-by":"publisher","first-page":"052102","DOI":"10.1007\/s11432-016-5541-9","volume":"59","author":"F Yan","year":"2016","unstructured":"Yan, F., Iliyasu, A., Hirota, K., Yang, H.: Strategy for quantum image stabilization. Sci. China Inf. Sci. 59, 052102 (2016)","journal-title":"Sci. China Inf. Sci."},{"issue":"4","key":"3435_CR13","doi-asserted-by":"publisher","first-page":"2162","DOI":"10.1007\/s10773-015-2855-0","volume":"55","author":"F Yan","year":"2016","unstructured":"Yan, F., Iliyasu, A., Khan, A., Yang, H.: Measurements-based moving target detection in quantum video. Int. J. Theor. Phys. 55(4), 2162\u20132173 (2016)","journal-title":"Int. J. Theor. Phys."},{"key":"3435_CR14","doi-asserted-by":"publisher","first-page":"1459","DOI":"10.1142\/S0219749911008015","volume":"9","author":"A Iliyasu","year":"2011","unstructured":"Iliyasu, A., Le, P., Dong, F., Hirota, K.: A framework for representing and producing movies on quantum computers. Int. J. Quan. Inform. 9, 1459\u20131497 (2011)","journal-title":"Int. J. Quan. Inform."},{"key":"3435_CR15","unstructured":"Iliyasu, A., Le, P., Dong, F., Hirota, K. Restricted geometric transformations and their applications for quantum image watermarking and authentication. In: Proceedings of the 10th Asian conference on quantum information science (2010)"},{"key":"3435_CR16","doi-asserted-by":"publisher","first-page":"1730001","DOI":"10.1142\/S0219749917300017","volume":"15","author":"F Yan","year":"2017","unstructured":"Yan, F., Iliyasu, A., Le, P.: Quantum image processing: a review of advances in its security technologies. Int. J. Quan. Inform. 15, 1730001 (2017)","journal-title":"Int. J. Quan. Inform."},{"key":"3435_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2020.106403","volume":"138","author":"B Abd-El-Atty","year":"2021","unstructured":"Abd-El-Atty, B., Iliyasu, A., Alanezi, A., et al.: Optical image encryption based on quantum walks. Opt. Lasers Eng. 138, 106403 (2021)","journal-title":"Opt. Lasers Eng."},{"key":"3435_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-32-9331-1","volume-title":"Quantum Image Processing","author":"F Yan","year":"2020","unstructured":"Yan, F., Venegas-Andraca, S.: Quantum Image Processing. Springer, Berlin (2020)"},{"key":"3435_CR19","doi-asserted-by":"publisher","first-page":"23864","DOI":"10.1109\/ACCESS.2018.2871107","volume":"7","author":"A Iliyasu","year":"2019","unstructured":"Iliyasu, A.: Roadmap to talking quantum movies: a contingent inquiry. IEEE Access 7, 23864\u201323913 (2019)","journal-title":"IEEE Access"},{"issue":"3","key":"3435_CR20","doi-asserted-by":"publisher","first-page":"1622","DOI":"10.1007\/s10773-015-2800-2","volume":"55","author":"J Wang","year":"2015","unstructured":"Wang, J.: QRDA: Quantum representation of digital audio. Int. J. Theor. Phys. 55(3), 1622\u20131641 (2015)","journal-title":"Int. J. Theor. Phys."},{"key":"3435_CR21","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.tcs.2017.12.025","volume":"752","author":"F Yan","year":"2018","unstructured":"Yan, F., Iliyasu, A., et al.: Flexible representation and manipulation of audio signals on quantum computers. Theoret. Comput. Sci. 752, 71\u201385 (2018)","journal-title":"Theoret. Comput. Sci."},{"key":"3435_CR22","doi-asserted-by":"publisher","first-page":"3242","DOI":"10.1007\/s10773-018-3841-0","volume":"57","author":"P Li","year":"2018","unstructured":"Li, P., Wang, B., Xiao, H., Liu, X.: Quantum representation and basic operations of digital signals. Int. J. Theor. Phys. 57, 3242\u20133270 (2018)","journal-title":"Int. J. Theor. Phys."},{"key":"3435_CR23","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/s11128-019-2317-3","volume":"18","author":"E Sahin","year":"2019","unstructured":"Sahin, E., Yilmaz, I.: QRMA: quantum representation of multichannel audio. Quant. Inf. Process. 18, 209 (2019)","journal-title":"Quant. Inf. Process."},{"key":"3435_CR24","doi-asserted-by":"publisher","first-page":"3457","DOI":"10.1103\/PhysRevA.52.3457","volume":"52","author":"A Barenco","year":"1995","unstructured":"Barenco, A., Bennett, C., Cleve, R., et al.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457\u20133467 (1995)","journal-title":"Phys. Rev. A"},{"key":"3435_CR25","volume-title":"Understanding Records","author":"J Hodgson","year":"2019","unstructured":"Hodgson, J.: Understanding Records, 2nd edn. Bloomsbury Pbulishing, London (2019)","edition":"2"},{"key":"3435_CR26","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/j.ins.2021.06.077","volume":"577","author":"F Yan","year":"2021","unstructured":"Yan, F., Li, N., Hirota, K.: QHSL: a quantum hue, saturation, and lightness color model. Inf. Sci. 577, 196\u2013213 (2021)","journal-title":"Inf. Sci."},{"issue":"8","key":"3435_CR27","doi-asserted-by":"publisher","first-page":"2833","DOI":"10.1007\/s11128-013-0567-z","volume":"12","author":"Y Zhang","year":"2013","unstructured":"Zhang, Y., Lu, K., Gao, Y., Wang, M.: NEQR: a novel enhanced quantum representation of digital images. Quan. Inf. Process. 12(8), 2833\u20132860 (2013)","journal-title":"Quan. Inf. Process."},{"issue":"2","key":"3435_CR28","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1007\/s11128-016-1463-0","volume":"16","author":"J Sang","year":"2017","unstructured":"Sang, J., Wang, S., Li, Q.: A novel quantum representation of color digital images. Quan. Inf. Process. 16(2), 42 (2017)","journal-title":"Quan. Inf. Process."},{"key":"3435_CR29","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1103\/PhysRevA.54.147","volume":"54","author":"V Vedral","year":"1996","unstructured":"Vedral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations. Phys. Rev. A 54, 147\u2013153 (1996)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"3435_CR30","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1063\/1.881299","volume":"44","author":"R Landeuer","year":"1991","unstructured":"Landeuer, R.: Information is physical. Phys. Today 44(5), 23\u201329 (1991)","journal-title":"Phys. Today"},{"issue":"2","key":"3435_CR31","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1007\/s10773-017-3580-7","volume":"57","author":"K Chen","year":"2018","unstructured":"Chen, K., Yan, F., Iliyasu, A., Zhao, J.: Exploring the implementation of steganography protocols on quantum audio signals. Int. J. Theor. Phys. 57(2), 476\u2013494 (2018)","journal-title":"Int. J. Theor. Phys."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03435-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-022-03435-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03435-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T18:30:16Z","timestamp":1648578616000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-022-03435-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,18]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["3435"],"URL":"https:\/\/doi.org\/10.1007\/s11128-022-03435-7","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,18]]},"assertion":[{"value":"2 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 February 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all authors, the corresponding author states that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"95"}}