Quantum steering refers to the non-classical correlations that can be
observed between the outcomes of measurements applied on half of an entangled
state and the resulting post-measured states that are left with the other
party. From an operational point of view, a steering test can be seen as an
entanglement test where one of the parties performs uncharacterised
measurements. Thus, quantum steering is a form of quantum inseparability that
lies in between the well-known notions of Bell nonlocality and entanglement.
Moreover, quantum steering is also related to several asymmetric quantum
information protocols where some of the parties are considered untrusted.
Because of these facts, quantum steering has received a lot of attention both
theoretically and experimentally. The main goal of this review is to give an
overview of how to characterise quantum steering through semidefinite
programming. This characterisation provides efficient numerical methods to
address a number of problems, including steering detection, quantification, and
applications. We also give a brief overview of some important results that are
not directly related to semidefinite programming. Finally, we make available a
collection of semidefinite programming codes that can be used to study the
topics discussed in this articleComment: v2: 31 pages, 2 figures. Published version. New material added.
Matlab codes to accompany this review can be found at https://git.io/vax9
