Super-Activation of Quantum Steering

TL;DR

This paper introduces a simple criterion for k-copy steerability of entangled states, demonstrating that many low-dimensional states become steerable when multiple copies are used, highlighting a super-activation effect.

Contribution

It provides an efficient condition for k-copy steerability and shows super-activation of steering in low-dimensional entangled states, suggesting entanglement and steering may become equivalent with multiple copies.

Findings

Any two-qubit and qubit-qutrit entangled states are k-copy steerable.

Super-activation allows unsteerable states to become steerable with multiple copies.

Results suggest entanglement and steering could be equivalent in the multi-copy regime.

Abstract

We consider Einstein-Podolsky-Rosen steering in the regime where the parties can perform collective measurements on many copies of a given shared entangled state. We derive a simple and efficient condition for guaranteeing that an entangled state is $k$-copy steerable. In particular we show that any two-qubit and qubit-qutrit entangled states is $k$-copy steerable. This allows us to discuss the effect of super-activation of steering, whereby an entangled state that is unsteerable (i.e., admits a local hidden state model) in the one-copy regime becomes $k$-copy steerable. We provide examples with few copies and low dimensions. Our results give evidence that entanglement and steering could become equivalent in the multi-copy regime.