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

TL;DR

This paper explores how local operations and classical communication between parties can reduce the entropic uncertainty lower bound in a tripartite quantum system, enhancing measurement precision with quantum memory.

Contribution

It introduces a cooperative strategy to minimize uncertainty bounds in a tripartite setting, linking the reduction to dense coding capacity and providing practical examples.

Findings

Lower bounds are reduced after information concentration.

The strategy improves measurement certainty in quantum systems.

Dense coding capacity offers a physical interpretation of the bounds.

Abstract

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 Charlie's lower bound about Alice's measurement outcomes. To this aim, they concentrate their correlation with Alice in Charlie's side via a cooperative strategy based on local operations and classical communication. We obtain lower bound for Charlie's uncertainty about Alice's 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.