2023/03/20 by Antonio F. Rotundo, Rotundo, Antonio F., René Schwonnek +1
Computer Science · #Computability, Logic, AI Algorithms #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2303.11382
openalex publication_date 2023/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of versatile generalizations of this relation. Our proof methods build on a deep connection between entropic uncertainties and interpolation inequalities for the doubly stochastic map that links probability distributions in two measurements bases. In contrast to the original relation, our generalization also incorporates the von Neumann entropy of the underlying quantum state. These results can be directly used to bound the extractable randomness of a source independent QRNG in the presence of fully quantum attacks, to certify entanglement between trusted parties, or to bound the entanglement of a system with an untrusted environment.