Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems

Abstract: Quantum steering is considered as one of the most well-known nonlocal phenomena in quantum mechanics. Unlike entanglement and Bell non-locality, the asymmetry of quantum steering makes it vital for one-sided device-independent quantum information processing. Although there has been much progress on steering detection for bipartite systems, the criterion for EPR steering in tripartite systems remains challenging and inadequate. In this paper, we firstly derive a novel and promising steering criterion for any three-qubit states via correlation matrix. Furthermore, we propose the monogamy relation between the tripartite steering of system and the bipartite steering of subsystems based on the derived criterion. Finally, as illustrations, we demonstrate the performance of the steering criterion and the monogamy relation by means of several representative examples. We believe that the results and methods presented in this work could be beneficial to capture genuine multipartite steering in the near future.