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.
On the distinguishability of random quantum states
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abstract
We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions, where n/d approaches a constant. In particular, for almost all ensembles of n states in n dimensions, p>0.72. An application to distinguishing Boolean functions (the "oracle identification problem") in quantum computation is given.
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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.