Detecting Einstein-Podolsky-Rosen steering through entanglement detection

TL;DR

This paper introduces a novel method to detect EPR steering in two-qubit states by transforming the problem into an entanglement detection task, simplifying the process and reducing experimental complexity.

Contribution

The authors propose a new criterion that detects EPR steerability via entanglement detection of a constructed state, avoiding steering inequalities and loopholes.

Findings

Detects EPR steering through entanglement of a constructed state.

Generalizes the criterion to higher-dimensional states.

Successfully applied to various mixed states.

Abstract

Quantum inseparabilities can be classified into three inequivalent forms: entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Bell-nonlocal states form a strict subset of EPR steerable states which also form a strict subset of entangled states. Recently, EPR steerable states are shown to be fundamental resources for one-sided device-independent quantum information processing tasks and, hence, identification of EPR steerable states becomes important from foundational as well as informational theoretic perspectives. In the present study we propose a new criteria to detect whether a given two-qubit state is EPR steerable. From an arbitrary given two-qubit state, another two-qubit state is constructed in such a way that the given state is EPR steerable if the new constructed state is entangled. Hence, EPR steerability of an arbitrary two-qubit state can be detected by detecting entanglement of the newly constructed state. Apart from providing a distinctive way to detect EPR steering without using any steering inequality, the novel finding in the present study paves a new direction to avoid locality loophole in EPR steering tests and to reduce the "complexity cost" present in experimentally detecting EPR steering. We also generalise our criteria to detect EPR steering of higher dimensional quantum states. Finally, we illustrate our result by using our proposed technique to detect EPR steerability of various families of mixed states.