{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T06:47:40Z","timestamp":1651560460284},"reference-count":19,"publisher":"Association for Computing Machinery (ACM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2002,7]]},"abstract":"\n We consider the possibility of encoding\n m<\/jats:italic>\n classical bits into many fewer\n n<\/jats:italic>\n quantum bits (qubits) so that an arbitrary bit from the original\n m<\/jats:italic>\n bits can be recovered with good probability. We show that nontrivial quantum codes exist that have no classical counterparts. On the other hand, we show that quantum encoding cannot save more than a logarithmic additive factor over the best classical encoding. The proof is based on an entropy coalescence principle that is obtained by viewing Holevo's theorem from a new perspective.In the existing implementations of quantum computing, qubits are a very expensive resource. Moreover, it is difficult to reinitialize existing bits during the computation. In particular, reinitialization is impossible in NMR quantum computing, which is perhaps the most advanced implementation of quantum computing at the moment. This motivates the study of quantum computation with restricted memory and no reinitialization, that is, of quantum finite automata. It was known that there are languages that are recognized by quantum finite automata with sizes exponentially smaller than those of corresponding classical automata. Here, we apply our technique to show the surprising result that there are languages for which quantum finite automata take exponentially more states than those of corresponding classical automata.\n <\/jats:p>","DOI":"10.1145\/581771.581773","type":"journal-article","created":{"date-parts":[[2003,1,10]],"date-time":"2003-01-10T14:31:05Z","timestamp":1042209065000},"page":"496-511","source":"Crossref","is-referenced-by-count":135,"title":["Dense quantum coding and quantum finite automata"],"prefix":"10.1145","volume":"49","author":[{"given":"Andris","family":"Ambainis","sequence":"first","affiliation":[{"name":"Institute for Advanced Study, Princeton, New Jersey"}]},{"given":"Ashwin","family":"Nayak","sequence":"additional","affiliation":[{"name":"California Institute of Technology, Pasadena, California"}]},{"given":"Amnon","family":"Ta-Shma","sequence":"additional","affiliation":[{"name":"Tel-Aviv University, Tel-Aviv, Israel"}]},{"given":"Umesh","family":"Vazirani","sequence":"additional","affiliation":[{"name":"University of California, Berkeley, California"}]}],"member":"320","reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing. 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IEEE Computer Society Press, Los Alamitos, Calif.","author":"Nayak A.","year":"1999"},{"issue":"7","key":"e_1_2_1_16_1","first-page":"324","article-title":"Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, England","volume":"7","author":"Nielsen M.","year":"2000","journal-title":"Chapter"},{"key":"e_1_2_1_17_1","volume-title":"Quantum Theory: Concepts and Methods","author":"Peres A.","year":"1995"},{"key":"e_1_2_1_18_1","unstructured":"Preskill J. 1998. Lecture notes. Available online at http:\/\/www.theory.caltech.edu\/people\/preskill\/ph229\/. Preskill J. 1998. Lecture notes. Available online at http:\/\/www.theory.caltech.edu\/people\/preskill\/ph229\/."},{"key":"e_1_2_1_19_1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1103\/RevModPhys.50.221","article-title":"General properties of entropy","volume":"50","author":"Wehrl A.","year":"1978","journal-title":"Rev. Mod. Phys."}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/581771.581773","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,4]],"date-time":"2021-03-04T09:44:29Z","timestamp":1614851069000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/581771.581773"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,7]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2002,7]]}},"alternative-id":["10.1145\/581771.581773"],"URL":"http:\/\/dx.doi.org\/10.1145\/581771.581773","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"value":"0004-5411","type":"print"},{"value":"1557-735X","type":"electronic"}],"subject":["Artificial Intelligence","Hardware and Architecture","Information Systems","Control and Systems Engineering","Software"],"published":{"date-parts":[[2002,7]]}}}