Tristan Nemoz

The amount of cryptographically secure randomness one can extract from a source can be linked to an optimization over conditional sandwiched Rényi entropies. Though these can be difficult to compute in general, we consider a simplified setting in which closed-form expressions can be obtained. More precisely, we consider a quantity we call the maximal intrinsic Rényi randomness and combine it with recent results on privacy amplification to derive simple expressions for the maximal quantity of $\epsilon$-secure randomness that can be extracted from finite uses of some memoryless source (which may be entangled with some eavesdropper). Overall this gives a simple method to compute this operationally relevant quantity and provides a benchmarking tool for the rates of finite size security proofs for randomness generation and quantum key distribution protocols. Along the way, we also prove closed-form expressions for the intrinsic randomness measured with respect to other Rényi entropy families.