{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T16:24:08Z","timestamp":1780331048129,"version":"3.54.1"},"reference-count":33,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T00:00:00Z","timestamp":1547596800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.<\/jats:p>","DOI":"10.3390\/e21010077","type":"journal-article","created":{"date-parts":[[2019,1,17]],"date-time":"2019-01-17T03:02:03Z","timestamp":1547694123000},"page":"77","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Logical Structures Underlying Quantum Computing"],"prefix":"10.3390","volume":"21","author":[{"given":"Federico","family":"Holik","sequence":"first","affiliation":[{"name":"Instituto de Fisica (IFLP-CCT-CONICET), Universidad Nacional de La Plata, C.C. 727, 1900 La Plata, Argentina"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3650-5858","authenticated-orcid":false,"given":"Giuseppe","family":"Sergioli","sequence":"additional","affiliation":[{"name":"Dipartimento di Pedagogia, Psicologia, Filosofia, Universit\u00e0 di Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hector","family":"Freytes","sequence":"additional","affiliation":[{"name":"Dipartimento di Pedagogia, Psicologia, Filosofia, Universit\u00e0 di Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Angel","family":"Plastino","sequence":"additional","affiliation":[{"name":"Instituto de Fisica (IFLP-CCT-CONICET), Universidad Nacional de La Plata, C.C. 727, 1900 La Plata, Argentina"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,16]]},"reference":[{"key":"ref_1","unstructured":"Nielsen, M.A., and Chuang, I.L. (2010). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1038\/s41534-016-0004-0","article-title":"Building logical qubits in a superconducting quantum computing system","volume":"3","author":"Gambetta","year":"2017","journal-title":"NPJ Quant. Inf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1002\/malq.201110030","article-title":"Quantum computational logic with mixed states","volume":"59","author":"Freytes","year":"2013","journal-title":"Math. Logic Q."},{"key":"ref_4","first-page":"1","article-title":"Probability in quantum computation and quantum computational logics: A survey","volume":"24","author":"Chiara","year":"2013","journal-title":"Math. Struct. Comp. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1640019","DOI":"10.1142\/S0219749916400190","article-title":"Abstract quantum computing machines and quantum computational logics","volume":"14","author":"Chiara","year":"2016","journal-title":"Int. J. Quant. Inf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/S0034-4877(15)60014-3","article-title":"Fuzzy approach for Toffoli gate in quantum computation with mixed states","volume":"74","author":"Freytes","year":"2014","journal-title":"Rep. Math. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.fss.2016.12.015","article-title":"A many-valued approach to quantum computational logics","volume":"335","author":"Chiara","year":"2016","journal-title":"Fuzzy Sets Syst."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chiara, M.L.D., Giuntini, R., Leporini, R., Freytes, H., and Sergioli, G. (2018). Probabilities and epistemic operations in the logics of quantum computation. Entropy, 20.","DOI":"10.3390\/e20110837"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.fss.2015.09.002","article-title":"A first-order epistemic quantum computational semantics with relativistic-like epistemic effects","volume":"298","author":"Chiara","year":"2016","journal-title":"Fuzzy Sets Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7349","DOI":"10.3390\/e17117349","article-title":"Quantum Information as a Non-Kolmogorovian Generalization of Shannon\u2019s Theory","volume":"17","author":"Holik","year":"2015","journal-title":"Entropy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"823","DOI":"10.2307\/1968621","article-title":"The logic of quantum mechanics","volume":"37","author":"Birkhoff","year":"1936","journal-title":"Ann. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.aop.2013.11.005","article-title":"A discussion on the origin of quantum probabilities","volume":"340","author":"Holik","year":"2014","journal-title":"Ann. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"052108","DOI":"10.1063\/1.3429619","article-title":"A quantum logical and geometrical approach to the study of improper mixtures","volume":"51","author":"Domenech","year":"2010","journal-title":"J. Math. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1007\/s10773-011-1037-y","article-title":"Convex quantum logic","volume":"51","author":"Holik","year":"2012","journal-title":"Int. J. Theor. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1836","DOI":"10.1007\/s10773-012-1277-5","article-title":"On the lattice structure of probability space in quantum mechanics","volume":"51","author":"Holik","year":"2013","journal-title":"Int. J. Theor. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"050502","DOI":"10.1103\/PhysRevLett.102.050502","article-title":"Computational Power of Correlations","volume":"102","author":"Anders","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","first-page":"021003","article-title":"Wigner Function Negativity and Contextuality in Quantum Computation on Rebits","volume":"5","author":"Delfosse","year":"2015","journal-title":"Phys. Rev. X"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1038\/nature13460","article-title":"Contextuality supplies the \u2019magic\u2019 for Quantum Computation","volume":"510","author":"Howard","year":"2014","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Raussendorf, R., Browne, D.E., Delfosse, N., Okay, C., and Bermejo-Vega, J. (arXiv, 2017). Contextuality and Wigner function negativity in qubit quantum computation, arXiv.","DOI":"10.1103\/PhysRevA.95.052334"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"022322","DOI":"10.1103\/PhysRevA.88.022322","article-title":"Contextuality in measurement-based quantum computation","volume":"88","author":"Raussendorf","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s10773-005-1490-6","article-title":"Kochen-Specker Theorem for von Neumann Algebras","volume":"44","year":"2005","journal-title":"Int. J. Theor. Phys."},{"key":"ref_22","first-page":"281","article-title":"Quantum computaton from a quantum logical perspective","volume":"7","author":"Bub","year":"2007","journal-title":"Quant. Inf. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.shpsb.2006.05.006","article-title":"Quantum probability theory","volume":"38","author":"Summers","year":"2007","journal-title":"Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Modern Phys."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kitaev, A.Y., Shen, A.H., and Vyalyi, M.N. (2002). Classical and Quantum Computation, American Mathematical Society Providence. Graduate Studies in Mathematics Volume 47.","DOI":"10.1090\/gsm\/047"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Aharanov, D., Kitaev, A., and Nisan, N. (1998, January 24\u201326). Quantum circuits with mixed states. Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, Dallas, TX, USA.","DOI":"10.1145\/276698.276708"},{"key":"ref_26","unstructured":"Kalmbach, G. (1983). Ortomodular Lattices, Academic Press."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Gudder, S.P. (1979). Stochastic Methods in Quantum Mechanics, Dover Publications.","DOI":"10.1016\/0034-4877(79)90056-9"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Khrennikov, A. (2010). Ubiquitous Quantum Structure-From Psychology to Finance, Springer.","DOI":"10.1007\/978-3-642-05101-2"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"20150094","DOI":"10.1098\/rsta.2015.0094","article-title":"Social Laser: Action amplifcation by stimulated emission of social energy","volume":"374","author":"Khrennikov","year":"2016","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1111\/tops.12042","article-title":"Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought","volume":"5","author":"Aerts","year":"2013","journal-title":"Top. Cognit. Sci."},{"key":"ref_31","unstructured":"Aharonov, D. (arXiv, 2003). A Simple Proof that Toffoli and Hadamard are Quantum Universal, arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Varadarajan, V. (1968). Geometry of Quantum Theory I, van Nostrand.","DOI":"10.1007\/978-1-4615-7706-5"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S1355-2198(00)00033-2","article-title":"Entanglement and Open Systems in Algebraic Quantum Field Theory","volume":"32","author":"Clifton","year":"2001","journal-title":"Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Modern Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/77\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:26:32Z","timestamp":1760185592000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/77"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,16]]},"references-count":33,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["e21010077"],"URL":"https:\/\/doi.org\/10.3390\/e21010077","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,16]]}}}