  We demonstrate how quantum optimal control can be used to enhance quantum
resources for bipartite one-way protocols, specifically EPR-steering with qubit
measurements. Steering is relevant for one-sided device-independent key
distribution, the realistic implementations of which necessitate the study of
noisy scenarios. So far mainly the case of imperfect detection efficiency has
been considered; here we look at the effect of dynamical noise responsible for
decoherence and dissipation. In order to set up the optimisation, we map the
steering problem into the equivalent joint measurability problem, and employ
quantum resource-theoretic robustness monotones from that context. The
advantage is that incompatibility (hence steerability) with arbitrary pairs of
noisy qubit measurements has been completely characterised through an
analytical expression, which can be turned into a computable cost function with
exact gradient. Furthermore, dynamical loss of incompatibility has recently
been illustrated using these monotones. We demonstrate resource control
numerically using a special gradient-based software, showing, in particular,
the advantage over naive control with cost function chosen as a fidelity in
relation to a specific target. We subsequently illustrate the complexity of the
control landscapes with a simplified two-variable scheme. The results
contribute to the theoretical understanding of the limitations in realistic
implementations of quantum information protocols, also paving way to practical
use of the rather abstract quantum resource theories.
