Activating the Violation of Steering Inequality for Two‐Qubit X States

Abstract

The phenomenon of superactivation of quantum steering, that is, the fact that by combining several copies of the unsteerable quantum state one can get a steerable quantum state, has recently attracted much attention. This property is currently only known for isotropic states, and whether there exists an example other than isotropic states is so far an open question. It is of great importance to learn the activation property of non-isotropic states. In this paper, it is shown that the violation of the local uncertainty relations (LUR) steering inequality can be activated for two-qubit X type entangled mixed states. Although the activation phenomenon proven in this paper cannot guarantee the superactivation of steering for two-qubit X states, it does provide clues for this goal. In addition, previous results indicate that two copies are enough for the superactivation of steering, while the price to pay is a high local dimension, and it is unclear whether superactivation is possible with few copies in low-dimensional systems such as two-qubit systems. By providing examples of activation of LUR steering inequality with two copies in a two-qubit system, the work may open a potential way to the solution of this question.