Quantification of Gaussian quantum steering

Abstract

Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible.

5 pages, 2 figures. Close to published version

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Cited by in corpus (14)

• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Classifying directional Gaussian quantum entanglement, EPR steering and discord
• Schur complement inequalities for covariance matrices and monogamy of quantum correlations
• Exploration quantum steering, nonlocality and entanglement of two-qubit X-state in structured reservoirs
• Manipulating the direction of Einstein-Podolsky-Rosen steering
• Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture
• Einstein-Podolsky-Rosen steering measure for two-mode continuous variable states
• Temporal Steering in Four Dimensions with applications to coupled qubits and magnetoreception
• Experimental nonlocal steering of Bohmian trajectories
• Investigating Einstein-Podolsky-Rosen steering of continuous variable bipartite states by non-Gaussian pseudospin measurements
• Swapping of Gaussian Einstein-Podolsky-Rosen steering
• Einstein-Podolsky-Rosen steering and Bell nonlocality of two macroscopic mechanical oscillators in optomechanical systems
• Genuine multipartite nonlocality of permutationally invariant Gaussian states
• Optimal secure quantum teleportation of coherent states of light