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Quantum Information Processing

Quantum correlations in Gaussian states via Gaussian channels: steering, entanglement, and discord

Zhongxiao Wang, Shuhao Wang, Qiting Li, Tie-Jun Wang, Chuan Xi Wang

Published Mar 1, 2016• 7 citations
Publisher
DOI
10.1007/s11128-016-1276-1

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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.
Beam splitters are important components in numerous tasks of quantum information protocols used either in simple or in an interferometric arrangement or together with other quantum systems. This report shows interesting aspects of the quantum correlations of two-mode Gaussian state (TMGS) for the photons retrieved via a linear beam splitter when they are initially employed at the input of either pure or mixed two single-mode Gaussian states (TSMGSs). The quantum correlations obey the boundaries of quantum non-locality, steering, entanglement and discord for pure input states. Though Bell inequality does not violate, quantum steering, entanglement and discord exist in the quantum state evolved by the beam splitter when input states become mixed. Specifically, the quantum steering, entanglement and discord persist to some degrees against the thermal photon number, the Bell inequality is, nonetheless, obeyed by the quantum state except in a very sharp regime.
In this study, we quantify quantum steering, quantum entanglement, and quantum discord and their interconnection using the technique of parametric down-conversion. Initially, two single-mode Gaussian states together with a non-linear crystal in a cavity are considered. The behavior of the three kinds of quantum correlations depend on the phase of the coherent pump field, purity, and non-classicality of the input states, and the damping rates of the cavity. The amount and time evolution of the quantum correlations enhances with the difference between the non-classicality of the initial states. In presence of the damping rates, the quantum steering and quantum entanglement (quantum discord) increase (decreases) with the purity of the input cavity field. We note that the amount and survival time of the quantum correlations can be controlled by varying the relative phase associated to the coherent pump field. The boundaries of the three kinds of quantum correlations are defined and explained with respect to each other, which form a hierarchy.