Classifying directional Gaussian quantum entanglement, EPR steering and discord

Quantum discord quantifies how much Alice's system is disrupted after a measurement is performed on Bob's. Conceptually, this behavior acts the same way as quantum steering and we find that the discord grows with better steering from Bob to Alice. Using Venn diagrams, the relations between the different classes of Gaussian continuous variable entanglement and the links to discord for the squeezed-thermal states are established. We identify a directional quantum teleportation task for each class of squeezed-thermal state entanglement, and establish a unified signature for quantum steering, entanglement and discord beyond entanglement. Quantum steering and discord are promising candidates to quantify the potential of the directional quantum tasks where Alice and Bob possess asymmetrically noisy channels.