Bipartite Steering Research Articles

Operator space approach to steering inequality

In Junge and Palazuelos (2011 Commun. Math. Phys. 306 695–746) and Junge et al (2010 Commun. Math. Phys. 300 715–39) the operator space theory was applied to study bipartite Bell inequalities. The aim of the paper is to follow this line of research and use the operator space technique to analyze the steering scenario. We obtain a bipartite steering functional with unbounded largest violation of steering inequality, as well as constructing all ingredients explicitly. It turns out that the unbounded largest violation is obtained by a non maximally entangled state. Moreover, we focus on the bipartite dichotomic case where we construct a steering functional with unbounded largest violation of steering inequality. This phenomenon is different to the Bell scenario where only the bounded largest violation can be obtained by any bipartite dichotomic Bell functional.

Role of thermal noise in tripartite quantum steering

The influence of thermal noise on bipartite and tripartite quantum steering induced by a short laser pulse in a hybrid three-mode optomechanical system is investigated. The calculation is carried out under the bad cavity limit, the adiabatic approximation of a slowly varying amplitude of the cavity mode, and with the assumption of driving the cavity mode with a blue detuned strong laser pulse. Under such conditions, explicit expressions of the bipartite and tripartite steering parameters are obtained, and the concept of collective tripartite quantum steering, recently introduced by He and Reid [Phys. Rev. Lett. 111, 250403 (2013)], is clearly explored. It is found that both bipartite and tripartite steering parameters are sensitive functions of the initial state of the modes and distinctly different steering behavior could be observed depending on whether the modes were initially in a thermal state or not. For the modes initially in a vacuum state, the bipartite and tripartite steering occur simultaneously over the entire interaction time. This indicates that collective tripartite steering cannot be achieved. The collective steering can be achieved for the modes initially prepared in a thermal state. We find that the initial thermal noise is more effective in destroying the bipartite rather than the tripartite steering which, on the other hand, can persist even for a large thermal noise. For the initial vacuum state of a steered mode, the tripartite steering exists over the entire interaction time even if the steering modes are in very noisy thermal states. When the steered mode is initially in a thermal state, it can be collectively steered by the other modes. There are thresholds for the average number of the thermal photons above which the existing tripartite steering appears as the collective steering. Finally, we point out that the collective steering may provide a resource in a hybrid quantum network for quantum secret sharing protocol.

Einstein-Podolsky-Rosen paradox and quantum steering in a three-mode optomechanical system

We study multi-partite entanglement, the generation of EPR states and quantum steering in a three-mode optomechanical system composed of an atomic ensemble located inside a single-mode cavity with a movable mirror. The cavity mode is driven by a short laser pulse, has a nonlinear parametric-type interaction with the mirror and a linear beamsplitter-type interaction with the atomic ensemble. There is no direct interaction of the mirror with the atomic ensemble. A threshold effect for the dynamics of the system is found, above which the system works as an amplifier and below which as an attenuator of the output fields. The threshold is determined by the ratio of the coupling strengths of the cavity mode to the mirror and to the atomic ensemble. It is shown that above the threshold the system effectively behaves as a two-mode system in which a perfect bipartite EPR state can be generated, while it is impossible below the threshold. Furthermore, a fully inseparable tripartite entanglement and even further a genuine tripartite entanglement can be produced above and below the threshold. In addition, we consider quantum steering and examine the monogamy relations that quantify the amount of bipartite steering that can be shared between different modes. It is found that the mirror is more capable for steering of entanglement than the cavity mode. The two way steering is found between the mirror and the atomic ensemble despite the fact that they are not directly coupled to each other, while it is impossible between the output of cavity mode and the ensemble which are directly coupled to each other.