Complementary relation between quantum entanglement and entropic uncertainty

Yun Cao,Dong Wang,Xiao-Gang Fan,Fei Ming,Zhang-Yin Wang,Liu Ye

Figure 1. The entropic uncertainty versus EOF $E\left(\left|\psi \right\rangle \right)$ for the two-qubit pure states $\left|\psi \right\rangle $. The red line (limit) is denoted by $U=S(X\left|B\right.)+S(Y\left|B\right.)+S(Z\left|B\right.)=2-2E\left(\left|\psi \right\rangle \right)$. The figure plots the entropic uncertainty (U) along the y-axis, and the EOF (E) along the x-axis, for 105 randomly two-qubit pure states.