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Min-entropy sampling gives a bound on the min-entropy of a randomly chosensubset of a string, given a bound on the min-entropy of the whole string.K\"onig and Renner showed a min-entropy sampling theorem that holds relative toquantum knowledge. Their result achieves the optimal rate, but it can only beapplied if the bits are sampled in blocks, and only gives weak bounds for thenon-smooth min-entropy. We give two new quantum min-entropy sampling theoremsthat do not have the above weaknesses. The first theorem shows that the resultby K\"onig and Renner also applies to bitwise sampling, and the second theoremgives a strong bound for the non-smooth min-entropy. Our results imply a newlower bound for k-out-of-n random access codes: while previous results byBen-Aroya, Regev, and de Wolf showed that the decoding probability isexponentially small in k if the storage rate is smaller than 0.7, our resultsimply that this holds for any storage rate strictly smaller than 1, which isoptimal.

Bitwise Quantum Min-Entropy Sampling and New Lower Bounds for Random Access Codes