Tight steering inequalities from generalized entropic uncertainty relations
Year: 2018
Type: article
Abstract: We establish a general connection between entropic uncertainty relations, Einstein-Podolsky-Rosen steering, and joint measurability. Specifically, we construct steering inequalities from any entropic uncertainty relation, given that the latter satisfies two natural properties. We obtain steering inequalities based on R\'enyi entropies. These turn out to be tight in many scenarios using max- and min-entropies. Considering steering tests with two noisy measurements, our inequalities exactly recover the noise threshold for steerability. This is the case for any pair of qubit two-outcome measurements as well as for pairs of mutually unbiased bases in any dimension. This shows that easy-to-evaluate quantities, such as entropy, can optimally witness steering, despite the fact that they are coarse-grained representations of the underlying statistics.
Source: Physical Review A
Institution: University of Geneva
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2885003376