Stronger entropic uncertainty relations with multiple quantum memories

Abstract

The uncertainty relation is the basic principle of quantum mechanics, limiting the information obtained when two arbitrary noncommutative measurements are made. In principle, the lower bound of uncertainty relation indicates the limit of uncertainty, therefore to obtain a tight and essential one is basically on demand and nontrivial. In this work, we propose a stronger tripartite entropic uncertainty relation with quantum memories by considering mutual information and Holevo quantity, being tighter than the existed ones. Besides, we generalize the tripartite scenario into a universal case, i.e., multipartite and multi-observable entropic uncertainty relation. Furthermore, the proposed tripartite EUR is well applied to security analysis of quantum key distribution (QKD) protocols and quantum randomness, attaining higher quantum secret key rates in QKD and to guarantee the desired randomness. Thus, it is believed that our investigations better shed light on the nature of the uncertainty, and are beneficial to practical quantum information processing.