Improving Einstein–Podolsky–Rosen steering inequalities with state information

• We look at how uncertainty relations affect resulting EPR-steering inequalities.
• Improving uncertainty relations doesnʼt always improve EPR-steering inequalities.
• We show this using Berta et al.ʼs uncertainty relation as an example.
• Information about the state can still be used to improve EPR-steering inequalities.
• We develop a new symmetric EPR-steering inequality this way.

We discuss the relationship between entropic Einstein–Podolsky–Rosen (EPR)-steering inequalities and their underlying uncertainty relations along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering inequalities. In particular, we discuss how using information about the state of a quantum system affects oneʼs ability to witness EPR-steering. As an example, we consider the recent improvement to the entropic uncertainty relation between pairs of discrete observables (Berta et al., 2010 [10]). By considering the assumptions that enter into the development of a steering inequality, we derive correct steering inequalities from these improved uncertainty relations and find that they are identical to ones already developed (Schneeloch et al., 2013 [9]). In addition, we consider how one can use state information to improve our ability to witness EPR-steering, and develop a new continuous variable symmetric EPR-steering inequality as a result.