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Phys Rev Lett. 2015 Feb 13;114(6):060402. Epub 2015 Feb 12.

Classifying directional Gaussian entanglement, Einstein-Podolsky-Rosen steering, and discord.

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State Key Laboratory of Mesoscopic Physics, School of Physics, Peking University, Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.
Centre for Quantum Atom Optics, Swinburne University of Technology, Melbourne, Australia.


Using Venn diagrams, we classify the different types of two-mode Gaussian continuous variable quantum correlation including directional entanglement and Einstein-Podolsky-Rosen (EPR) steering. We establish unified signatures for one- and two-way quantum steering, entanglement, and discord beyond entanglement in terms of an EPR-type variance. By focusing on Gaussian states, we link an optimized condition for entanglement based on an EPR variance to the Simon-Peres condition. This allows us to quantify the asymmetry of the Gaussian entanglement, and to relate the asymmetry to a directional quantum teleportation protocol where Alice and Bob possess asymmetrically noisy channels. Our analysis enables a determination of the type and direction of quantum correlation in a way that is easily measured in experiment. We also find that for symmetric states, when discord exceeds a certain threshold, the states are necessarily steerable.

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