Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata

Details Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata

1998-04-18

arxiv.org/abs/quant-ph/9804043v2

Physics

Quantum Physics

12 pages, 3 figures. Defines random access codes, gives upper and lower bounds for the number of bits required for such (possi

Scientific paper

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.

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