an:06504129
Zbl 1323.81011
Schneeloch, James; Broadbent, Curtis J.; Howell, John C.
Improving Einstein-Podolsky-Rosen steering inequalities with state information
EN
Phys. Lett., A 378, No. 10, 766-769 (2014).
00349644
2014
j
81P40 81P45 94A17
EPR-steering; entanglement; EPR-paradox; uncertainty relations; entropy
Summary: 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 one's ability to witness EPR-steering. As an example, we consider the recent improvement to the entropic uncertainty relation between pairs of discrete observables [\textit{M. Berta} et al., ``The uncertainty principle in the presence of quantum memory'', Nat. Phys. 6, 659--662 (2010; \url{doi:10.1038/nphys1734})]. 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 [\textit{J. Schneeloch} et al., ``Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations'', Phys. Rev. A (3) 87, No. 6, Article ID 062103 (2013; \url{doi:10.1103/PhysRevA.87.062103})]. 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.