Reducing the entropic uncertainty lower bound in the presence of quantum memory via local operation and classical communication

The uncertainty principle sets lower bound on the uncertainties of two incompatible observables measured on a particle. The uncertainty lower bound can be reduced by considering a particle as a quantum memory entangled with the measured particle. In this paper, we consider a tripartite scenario in which a quantum state has been shared between Alice, Bob, and Charlie. The aim of Bob and Charlie is to minimize Charlies lower bound about Alices measurement outcomes. To this aim, they concentrate their correlation with Alice in Charlies side via a cooperative strategy based on local operations and classical communication. We obtain lower bound for Charlies uncertainty about Alices measurement outcomes after concentrating information and compare it with the lower bound without concentrating information in some examples. We also provide a physical interpretation of the entropic uncertainty lower bound based on the dense coding capacity.