Quantum-Memory-Assisted Entropic Uncertainty in Two-Qubit Heisenberg XX Spin Chain Model

We have studied the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in two-qubit Heisenberg XX spin chain model with Dzyaloshinskii-Moriya (DM) interaction and external magnetic field. It shows that the DM interaction |Dz| and the spin interaction |J| can efficiently suppress the entropic uncertainty of Pauli observables (σx and σz), even make the entropic uncertainty close to zero. The external magnetic field that acts on the two spin sites along z-direction leads to two different effects on entropic uncertainty under the different thermal equilibrium temperature. Furthermore, the dynamic features of entropic uncertainty with DM interactions and spin interactions under intrinsic decoherence condition are investigated. We find that when the Werner state acts as initial state, the larger purity parameter can yield smaller value of entropic uncertainty at the initial evolution time. And the entropic uncertainty of the XX model with DM interaction in z-direction is independent of external magnetic field \({\mathscr{B}}\). We also verified the entropic uncertainty is anti-correlated with the quantum discord of the spin chain system in full evolution time. Meanwhile, DM interactions and the spin interactions can make the evolutions of entropic uncertainty and its lower bound oscillate with evolution time, and the increasing of strengthen of DM interactions and spin interactions can lead to an increasing of oscillation frequency, and the variations of amplitudes are different for these two kinds of interactions. Especially, when the strength of spin interaction is larger, the trends of entropic uncertainty and its lower bound can be changed from oscillation to smoothness, which can be regarded as there is no DM interaction.