We consider the possibility of encoding m classical bits into much fewer n quantum bits so that an arbitrary bit from the original m bits can be recovered with a good probability, and we show that non-trivial quantum encodings exist that have no classical counterparts. On the other hand, we show that quantum encodings cannot be much more succint as compared to classical encodings, and we provide a lower bound on such quantum encodings. Finally, using this lower bound, we prove an exponential lower bound on the size of 1-way quantum finite automata for a family of languages accepted by linear sized deterministic finite automata.
|Number of pages||8|
|Journal||Conference Proceedings of the Annual ACM Symposium on Theory of Computing|
|State||Published - 1999|
|Event||Proceedings of the 1999 31st Annual ACM Symposium on Theory of Computing - FCRC '99 - Atlanta, GA, USA|
Duration: 1 May 1999 → 4 May 1999