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