  Quantum correlations and Wigner negativity are two important signatures of
nonclassicality in continuous-variable quantum systems. In this work, we
investigate how both are intertwined in the context of the conditional
generation of Wigner negativity. It was previously shown that when Alice and
Bob share a Gaussian state, Bob can perform some measurement on his system to
create Wigner negativity on Alice's side if and only if there is Gaussian
steering from Alice to Bob. In this work, we attempt to generalise these
findings to a much broader class of scenarios on which Alice and Bob share a
non-Gaussian state. We show that if Alice can initially steer Bob's system with
Wigner-positive measurements, Bob can remotely create Wigner negativity in
Alice's subsystem. Even though this shows that quantum steering is sufficient,
we also show that quantum correlations are in general not necessary for the
conditional generation of Wigner negativity.
