Quantum-memory-assisted entropic uncertainty relation induced by encoding entanglement in two semiconductor microcavities

The quantum-memory-assisted entropic uncertainty relation (QMA-EUR) plays an important role in quantum information theory, as it provides insights into the fundamental limits of measurement accuracy in entangled quantum systems. This paper investigates the QMA-EUR, which is activated by the entanglement between two quantum dots (QDs) confined in semiconductor microcavities that are coupled by an optical fiber. The investigation focuses on the dynamic characteristics of the QMA-EUR under the effects of dissipation. Moreover, two distinct initial states of the two QDs are examined: correlated and uncorrelated. In the initial uncorrelated state, the evolution of the QMA-EUR and entanglement is influenced by the coupling strengths between the QDs and cavities, as well as between the fiber and cavities, and by the detuning. In contrast, if the two QDs are initially in a maximally correlated state, these couplings and the detuning considerably increase the stability of both the entanglement and the QMA-EUR. They also extend the time intervals during which Alice can precisely predict the measurement results. Notably, strong couplings, in conjunction with an initially maximally entangled state, increase the robustness of the quantum memory mechanism.