Improving Einstein-Podolsky-Rosen Steering Inequalities with State Information

Abstract

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 the intrinsic uncertainty in a mixed quantum state is used to improve existing uncertainty relations and how this information affects one's ability to witness EPR-steering. As an example, we consider the recent improvement (using a quantum memory) to the entropic uncertainty relation between pairs of discrete observables (Nat. Phys. 6, 659 (2010)) and show that a trivial substitution of the tighter bound in the steering inequality leads to contradictions, due in part to the fact that the improved bound depends explicitly on the state being measured. 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 (Phys. Rev. A, 87, 062103 (2013)). In addition, we consider how one can use the information about the quantum state to improve our ability to witness EPR-steering, and develop a new symmetric EPR-steering inequality as a result.

6 pages

References in corpus (5)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Improved entropic uncertainty relations and information exclusion relations
• Majorization entropic uncertainty relations
• Improved bounds in entropic uncertainty relations
• The Relationship Between Discrete and Continuous Entropy in EPR-Steering Inequalities

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• General entropy-like uncertainty relations in finite dimensions
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Entropic uncertainty relations for successive measurements of canonically conjugate observables
• Experimental implementation of the optical fractional Fourier transform in the time-frequency domain
• Improved quantum entropic uncertainty relations
• Entropic measures of joint uncertainty: effects of lack of majorization
• Uncertainty-Reality Complementarity and Entropic Uncertainty Relations
• Steering and correlations for the single qudit state on the example of $j=3/2$
• Optimal Universal Uncertainty Relations
• Some applications of uncertainty relations in quantum information
• Steering in spin tomographic probability representation