The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski–Moriya interaction

The effects of mixedness and entanglement on the lower bound and tightness of the entropic uncertainty in the Heisenberg model with Dzyaloshinski–Moriya (DM) interaction have been investigated. It is found that the mixedness can reflect the essence of the entropic uncertainty better than the entanglement. Meanwhile, the uncertainty of measurement results will be reduced by the entanglement and improved by the mixedness. The entanglement can destroy the tightness of the uncertainty, while the tightness will be improved with the increase in the mixedness. In addition, the tightness of the uncertainty in Heisenberg model can be expressed as a function of the magnetic properties, the strength of the DM interaction as well as the mixedness of the state and the functional form has no relationship with temperature. What’s more, the entropic uncertain inequality becomes uncertain equality when the mixedness of the system reaches the minimum value. For a given mixedness, the tightness will be reduced with the increase in the strength of DM interaction at the antiferromagnetic case while the situation is just the opposite for the ferromagnetic case.