Dense quantum coding and a lower bound for 1-way quantum automata
Andris Ambainis, Ashwin Nayak, Amnon Ta‐Shma, Umesh V. Vazirani · 1999
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 an the size of l-way quantum linite automata for a family of languages accepted by linear sized deterministic linite automata.