Gereon Koßmann

We present a numerical framework for the reliable estimation of conditional von Neumann entropy in device-independent quantum cryptography and randomness extraction sceratios. By leveraging a hierarchy of semidefinite programs derived from the Navascués--Pironio--Acín (NPA) hierarchy, our method efficiently computes entropy bounds based solely on observed statistics, under the assumption that quantum mechanics holds true. Our approach is built on a recent integral representation presented by [Frenkel, Quantum 7, 1102 (2023)] and extends the landscape of methods for computing provable lower bounds on the conditional von Neumann entropy. Notably, it requires approximately half as many support variables compared to the Brown--Fawzi--Fawzi method, with the additional advantage that these variables can be chosen projectively. The method facilitates the derivation of provable bounds on extractable randomness even in noisy scenarios and aligns with modern entropy accumulation theorems. This makes our framework a versatile tool for practical quantum cryptographic protocols, broadening the possibilities for secure communication in untrusted environments.