Quantum-memory-assisted entropic uncertainty principle, teleportation and entanglement witness in structured reservoirs

TL;DR

This paper explores how quantum-memory-assisted entropic uncertainty relates to quantum teleportation and entanglement detection in structured reservoirs, providing geometric insights and criteria for usefulness and witnessing of entanglement.

Contribution

It establishes a geometric connection between entropic uncertainty bounds and teleportation capability, and analyzes entanglement witnessing in bosonic structured reservoirs.

Findings

States lowering the uncertainty bound are useful for teleportation.

Entanglement can be witnessed without explicit spectral density dependence.

Different estimates identify entanglement regions in reservoirs.

Abstract

We relate the principle of quantum-memory-assisted entropic uncertainty to quantum teleportation and show geometrically that any two-qubit state which lowers the upper bound of this uncertainty relation is useful for teleportation. We also explore the efficiency of this entropic uncertainty principle on witnessing entanglement in a general class of bosonic structured reservoirs. The entanglement regions witnessed by different estimates are determined, which may have no relation with the explicit form of the spectral density of the reservoir for certain special chosen sets of the initial states.