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The term Einstein-Podolsky-Rosen steering refers to a quantum correlationintermediate between entanglement and Bell nonlocality, which has beenconnected to another fundamental quantum property: measurement incompatibility.In the finite-dimensional case, efficient computational methods to quantifysteerability have been developed. In the infinite-dimensional case, however,less theoretical tools are available. Here, we approach the problem ofsteerability in the continuous variable case via a notion of state-channelcorrespondence, which generalizes the well-known Choi-Jamio\l{}kowskicorrespondence. Via our approach we are able to generalize the connectionbetween steering and incompatibility to the continuous variable case and toconnect the steerability of a state with the incompatibility breaking propertyof a quantum channel, e.g., noisy NOON states and amplitude damping channels.Moreover, we apply our methods to the Gaussian steering setting, proving, amongother things, that canonical quadratures are sufficient for steering Gaussianstates.

Continuous variable steering and incompatibility via state-channel duality