Einstein-Podolsky-Rosen Steering and Quantum Steering Ellipsoids: Optimal Two-Qubit States and Projective Measurements

TL;DR

This paper identifies optimal two-qubit states and measurements that maximize EPR steering and the volume of the quantum steering ellipsoid, providing insights for quantum cryptography under noise.

Contribution

It introduces a novel method using the quantum steering ellipsoid to find optimal measurements for EPR steering and characterizes states useful for one-sided device-independent quantum cryptography.

Findings

Maximized EPR steering quantifiers for specific state families.

Developed a new approach to determine optimal measurements via the QSE.

Identified states optimal for quantum cryptography under noise.

Abstract

We identify the families of states that maximise some recently proposed quantifiers of Einstein-Podolsky-Rosen (EPR) steering and the volume of the Quantum Steering Ellipsoid (QSE). The optimal measurements which maximise genuine EPR steering measures are discussed and we develop a novel way to find them using the QSE. We thus explore the links between genuine EPR steering and the QSE and introduce states that can be the most useful for one-sided device-independent quantum cryptography for a given amount of noise.