{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T10:15:28Z","timestamp":1648548928412},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,28]],"date-time":"2014-03-28T00:00:00Z","timestamp":1395964800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>Quantum computation and quantum computational logics give rise to some non-standard probability spaces that are interesting from a formal point of view. In this framework, <jats:italic>events<\/jats:italic> represent quantum pieces of information (<jats:italic>qubits<\/jats:italic>, <jats:italic>quregisters<\/jats:italic>, <jats:italic>mixtures of quregisters<\/jats:italic>), while operations on events are identified with <jats:italic>quantum logic gates<\/jats:italic> (which correspond to dynamic reversible quantum processes). We investigate the notion of <jats:italic>Shi\u2013Aharonov quantum computational algebra<\/jats:italic>. This structure plays the role for quantum computation that is played by \u03c3-complete Boolean algebras in classical probability theory.<\/jats:p>","DOI":"10.1017\/s0960129512000734","type":"journal-article","created":{"date-parts":[[2014,4,1]],"date-time":"2014-04-01T09:43:16Z","timestamp":1396345396000},"source":"Crossref","is-referenced-by-count":4,"title":["Probability in quantum computation and quantum computational logics: a survey"],"prefix":"10.1017","volume":"24","author":[{"given":"MARIA LUISA","family":"DALLA CHIARA","sequence":"first","affiliation":[]},{"given":"ROBERTO","family":"GIUNTINI","sequence":"additional","affiliation":[]},{"given":"GIUSEPPE","family":"SERGIOLI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,28]]},"reference":[{"key":"S0960129512000734_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9480-6"},{"key":"S0960129512000734_ref5","first-page":"213","volume-title":"Trends in Logic: 50 years of Studia Logica","author":"Dalla Chiara","year":"2003"},{"key":"S0960129512000734_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-10003-2_104"},{"key":"S0960129512000734_ref6","doi-asserted-by":"publisher","DOI":"10.1142\/S0219749905000943"},{"key":"S0960129512000734_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s10701-010-9407-5"},{"key":"S0960129512000734_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s10701-009-9302-0"},{"key":"S0960129512000734_ref2","doi-asserted-by":"publisher","DOI":"10.1145\/276698.276708"},{"key":"S0960129512000734_ref15","volume-title":"Quantum Computation and Quantum Information","author":"Nielsen","year":"2000"},{"key":"S0960129512000734_ref16","unstructured":"Shi Y. (2002) Both Toffoli and controlled-Not need little help to do universal quantum computation. arXiv:quant-ph\/0205115."},{"key":"S0960129512000734_ref13","volume-title":"States, effects and operations","author":"Kraus","year":"1983"},{"key":"S0960129512000734_ref3","first-page":"87","article-title":"Quantum computational structures.","volume":"54","author":"Cattaneo","year":"2004","journal-title":"Mathematica Slovaca"},{"key":"S0960129512000734_ref12","doi-asserted-by":"publisher","DOI":"10.1070\/RM1997v052n06ABEH002155"},{"key":"S0960129512000734_ref9","unstructured":"Dawson C. M. and Nielsen M. A. (2005) The Solovay\u2013Kitaev algorithm. arXiv.org:quant-ph\/0505030."},{"key":"S0960129512000734_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-7202-2"},{"key":"S0960129512000734_ref1","unstructured":"Aharonov D. (2003) A simple proof that Toffoli and Hadamard are quantum universal. arXiv:quant-ph\/0301040."},{"key":"S0960129512000734_ref11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023327005274"},{"key":"S0960129512000734_ref10","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1989.0099"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129512000734","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T19:43:07Z","timestamp":1555962187000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129512000734\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,28]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["S0960129512000734"],"URL":"https:\/\/doi.org\/10.1017\/s0960129512000734","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,28]]},"article-number":"e240306"}}