Every quantum random access code can be decoded with one measurement to a string that differs from the original in at most 2p(1-p)n positions, even for worst-case inputs.
Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata
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abstract
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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Getting almost all the bits from a quantum random access code
Every quantum random access code can be decoded with one measurement to a string that differs from the original in at most 2p(1-p)n positions, even for worst-case inputs.