Entropic Position-Momentum Uncertainty Relations for finite Key Analysis in Continuous Variable Quantum Key Distribution

Volkher B. Scholz [1,2], Fabian Furrer [1], Torsten Franz [1], Mario Berta [2], Marco Tomamichel [2,3], Matthias Christandl [2], Reinhard F. Werner [1]

[1] Institute for Theoretical Physics, University of Hannover
[2] Institute for Theoretical Physics, ETH Zurich
[3] Centre for Quantum Technologies, National University of Singapore

Entropic uncertainty relations quantify the quantum uncertainty principle in an information theoretic way, by measuring our uncertainty about the outcome distribution of measurements on some quantum system using entropic quantities. We study various such quantities and derive uncertainty relations for continuous outcome alphabets. Our motivation stems from the applicability to the security analysis of Continuous Variable Quantum Key Distribution.