2007/10/31 by Stephanie Wehner, Andreas Winter
Computer Science · Engineering · Physics and Astronomy · #Binary number #Binary relation #Entropic uncertainty #Entropy (arrow of time) #Observable #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Set (abstract data type) #Uncertainty principle #Wireless Communication Security Techniques #quant-ph
paper · pdf · doi:10.1063/1.2943685
published as Journal of Mathematical Physics, 49, 062105 (2008) · 8 pages revtex, 2 figures, v2: published version but with figures, min-entropy relation added
openalex publication_date 2008/06/01 · arxiv created 2008/08/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Uncertainty relations provide one of the most powerful formulations of the quantum mechanical principle of complementarity. Yet, very little is known about such uncertainty relations for more than two measurements. Here, we show that sufficient unbiasedness for a set of binary observables, in the sense of mutual anticommutation, is good enough to obtain maximally strong uncertainty relations in terms of the Shannon entropy. We also prove nearly optimal relations for the collision entropy. This is the first systematic and explicit approach to finding an arbitrary number of measurements for which we obtain maximally strong uncertainty relations. Our results have immediate applications to quantum cryptography.