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

Understand

Min-entropy sampling gives a bound on the min-entropy of a randomly chosen subset 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 to quantum knowledge.
• Their result achieves the optimal rate, but it can only be applied if the bits are sampled in blocks, and only gives weak bounds for the non-smooth min-entropy.
• We give two new quantum min-entropy sampling theorems that do not have the above weaknesses.