Study On Entropic Uncertainty Relation Of A Qubit-qutrit Heisenberg Spin Model And Its Steering

The quantum-memory-assisted entropic uncertainty relation(QMA-EUR)which derived from the Heisenberg uncertainty principle can be used as the witness of entanglement,while quantum coherence is the embodiment of the essence of entanglement.We investigate the QMA-EUR during a Heisenberg XYZ mixedspin(1/2,1)model with Dzyaloshinski-Moriya(DM)interaction in non-uniform magnetic fields.Entangling evolution in intrinsic decoherence and thermal equilibrium states is studied respectively.Furthermore,the entropy uncertainty relation is compared with other quantum correlation measures.And the results show that the coherence of the system is negatively correlated with the entropy uncertainty.The hybrid system can be controlled more easily than the spin-1 system,in the meantime it can encode more quantum information than the spin 1/2 system.QMA-EUR is related to the selection of measurement operator.Coupling strength,DM interaction and magnetic field strength can play a positive role in regulating the entropy uncertainty under the condition of fixing other parameters,when the measurement operator of the system is selected as the Pauli operator in x and z directions,which means they are conducive to the preservation of entanglement.In addition,the effects of weak measurement reversal(WMR)operation and local parity-time(PT)symmetric operation on the steering of entropic uncertainty are analyzed in non-maximally entangled states.The entropy uncertainty can be effectively reduced by selecting a specific weak measurement inversion intensity and more entangled resources can be detected when the appropriate PT symmetry parameters are selected within a certain time.