Quantum steering: a review with focus on semidefinite programming

TL;DR

This review discusses quantum steering, a form of quantum correlation between entangled states, emphasizing its characterization via semidefinite programming and its significance in quantum information protocols.

Contribution

It provides a comprehensive overview of characterizing quantum steering using semidefinite programming, including numerical methods, detection, and quantification techniques.

Findings

Semidefinite programming offers efficient tools for steering detection.

Quantum steering bridges entanglement and Bell nonlocality.

Codes for semidefinite programming are made publicly available.

Abstract

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 article