### Dense quantum coding and quantum finite automataDense quantum coding and quantum finite automata

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 Author Ambainis, Andris ♦ Nayak, Ashwin ♦ Ta-Shma, Amnon ♦ Vazirani, Umesh Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2002 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Automaton size ♦ Communication complexity ♦ Encoding ♦ Finite automata ♦ Quantum communication ♦ Quantum computation Abstract We consider the possibility of encoding $\textit{m}$ classical bits into many fewer $\textit{n}$ quantum bits (qubits) so that an arbitrary bit from the original $\textit{m}$ 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. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2002-07-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 49 Issue Number 4 Page Count 16 Starting Page 496 Ending Page 511

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Source: ACM Digital Library