Steering Criteria via Covariance Matrices of Local Observables in Arbitrary Dimensional Quantum Systems

Abstract

We derive steerability criteria applicable for both finite and infinite dimensional quantum systems using covariance matrices of local observables. We show that these criteria are useful to detect a wide range of entangled states particularly in high dimensional systems and that the Gaussian steering criteria for general M x N-modes of continuous variables are obtained as a special case. Extending from the approach of entanglement detection via covariance matrices, our criteria are based on the local uncertainty principles incorporating the asymmetric nature of steering scenario. Specifically, we apply the formulation to the case of local orthogonal observables and obtain some useful criteria that can be straightforwardly computable, and testable in experiment, with no need for numerical optimization.

6 pages with further "Remarks" and "Acknowledgement" added

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Cited by in corpus (10)

• Quantum Steering
• Quantum steering of Gaussian states via non-Gaussian measurements
• Uncertainty Relations for coarse-grained measurements: an overview
• Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems
• Certification of non-Gaussian Einstein-Podolsky-Rosen Steering
• Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Averaged fidelity-based steering criteria
• Parameterized steering criteria via correlation matrices
• Imprecise quantum steering inequalities in tripartite systems