Steering criteria from general entropic uncertainty relations

The effect of steering describes a possible action at a distance via measurements but characterizing the quantum states that can be used for this task remains difficult. We provide a method to derive sufficient criteria for steering from entropic uncertainty relations using generalized entropies. We demonstrate that the resulting criteria outperform existing criteria in several scenarios; moreover, they allow one to detect weakly steerable states.

Figure 1

The critical value of white noise $\alpha$ for different dimensions $d$, considering a complete set of MUBs. In this plot, blue circles correspond to our criterion in Eq. (19) for $q\to 1$ and the yellow squares to $q=2$. The green diamonds correspond to the results for the inequality presented in Ref. [37] and the red triangles in Ref. [38], where ${\alpha }_{\mathrm{crit}}$ was calculated via semidefinite programming (numerical method). Below the purple reversed triangles the existence of an LHS model for all projective measurements (i.e., infinite amount of measurements instead of $d+1$ MUBs) is known [2]. Note that Ref. [2] is given for comparison; this is not a steering criterion, but a bound on any criterion.