Analyzing entropic uncertainty bound in two qubits coupled to a spin environment

Abstract

By assuming a general pure state and a mixed Werner state as two initial states, we investigate the time evolution of entropic uncertainty bound in the presence of quantum memory for a two-qubit system interacting with an XY spin chain regarded as an environment constrained to carry the energy current. We obtain an explicit relationship between the entropic uncertainty bound and decoherence factor, and analytically study the dynamical process of entropic uncertainty bound for both weak and strong-coupling cases in two initial states. Our results reveal that the evolution of entropic uncertainty bound depends not only on the energy current, the system-environment couplings and the anisotropy parameter but also on the size of the environmental XY spin chain. Interestingly, we find that the entropic uncertainty bound can be suppressed by reducing the energy current on the environmental spin chain in a weak-coupling region, however, it has no sensitivity to the energy current in a strong-coupling region.