Relationship between quantum-memory-assisted entropic uncertainty and steered quantum coherence in a two-qubit X state

Quantum-memory-assisted entropic uncertainty relation is an upgrade version of the original entropic uncertainty relation with help of the quantum correlations between the measured subsystem and memory one. In this work, we analyze quantum-memory-assisted entropic uncertainty (QMA-EU) and steered quantum coherence (SQC) for an arbitrary two-qubit X-state, and then we get analytically an explicit relation between the QMA-EU and SQC. As an example, we consider the two interacting two-level atomic systems coupled to independent dissipative environments and investigate dynamics of QMA-EU and SQC of atomic systems in terms of the various values of atomic coupling parameters, environmental factors and frequency detune between the two-level atoms and environmental modes. The results show that the QMA-EU for Pauli observable set is anti-correlated to the SQC in an arbitrary two-qubit X-state, strictly. As well, the sum of QMA-EU and SQC is merely related with the reduced quantum entropies of the subsystem. In the dissipative environment, the QMA-EU and SQC of two-qubit atomic system still exhibit strict anti-correlation relationship in all the evolution time, which is quite different from the connections between QMA-EU and quantum correlation measured by concurrence. Furthermore, the QMA-EU can be suppressed and SQC can be improved with increasing of coupling parameters and detuning amount in non-Markovian environments, effectively. The optimal atomic state can be denoted by the values of the trough of wave during the oscillation of QMA-EU and SQC.