All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering

TL;DR

This paper introduces an all-versus-nothing proof of Einstein-Podolsky-Rosen steering, providing a new criterion for steerability that does not rely on inequalities, thus enhancing understanding and experimental testing of quantum nonlocality.

Contribution

It presents a novel inequality-free proof of EPR steering and a practical criterion for steerability in two-qubit states, advancing the theoretical and experimental framework.

Findings

Existence of steerable states not violating known inequalities

A new criterion based on projective measurements for steerability

An equivalent steering inequality to the all-versus-nothing proof

Abstract

Einstein-Podolsky-Rosen steering is a form of quantum nonlocality intermediate between entanglement and Bell nonlocality. Although Schr\"odinger already mooted the idea in 1935, steering still defies a complete understanding. In analogy to "all-versus-nothing" proofs of Bell nonlocality, here we present a proof of steering without inequalities rendering the detection of correlations leading to a violation of steering inequalities unnecessary. We show that, given any two-qubit entangled state, the existence of certain projective measurement by Alice so that Bob's normalized conditional states can be regarded as two different pure states provides a criterion for Alice-to-Bob steerability. A steering inequality equivalent to the all-versus-nothing proof is also obtained. Our result clearly demonstrates that there exist many quantum states which do not violate any previously known steering inequality but are indeed steerable. Our method offers advantages over the existing methods for experimentally testing steerability, and sheds new light on the asymmetric steering problem.