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

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.

5 pages and 4 figures

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• Quantum-memory-assisted entropic uncertainty relations
• Effects of Hawking radiation on the entropic uncertainty in a Schwarzschild space-time
• Multipartite steering inequalities based on entropic uncertainty relations
• Tightening the tripartite quantum memory assisted entropic uncertainty relation
• Tight entropic uncertainty relations for systems with dimension three to five
• Controlling the entropic uncertainty lower bound in two-qubit systems under the decoherence
• Spin-orbit-coupled quantum memory of a double quantum dot
• Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole
• Holevo bound of entropic uncertainty relation under Unruh channel in the context of open quantum systems
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements