Figure 3
From: Experimental test of fine-grained entropic uncertainty relation in the presence of quantum memory
Experimental results and theoretical predictions. (a) Theoretical predictions and experimental results for the Berta’s uncertainty bound and fine-grained uncertainty relation. The purple and green curve surfaces show the theoretical predictions of fine-grained uncertainty \(H({p}_{d}^{{\sigma }_{Z}})+H({p}_{d}^{S})\) and Berta’s uncertainty bound \({\mathrm{log}}_{2}\frac{1}{c}+S(A|B)\) for different θ and ϕ respectively (θ and ϕ are in the unit of radian). The blue and red spheres represent the experimental results of them separately. (b) and (c) represent the special case when ϕ = 1.57 and ϕ = 6.28. The purple and green solid line represent the theoretical predictions with ideal state. The blue and red solid circles represent the corresponding experiment results. In this experiment, the minimum value of \(H({p}_{d}^{S})\) occurs in this case for θ = 1.57, ϕ = 6.28, yielding the lower bound of inequality (5), \(H({p}_{d}^{{\sigma }_{Z}})+H({p}_{inf}^{S})\approx 1.69\), and our experimental result is 1.70. It can be seen that our experimental results coincide with the theoretical predictions very well.
