Quantum resource control for noisy Einstein-Podolsky-Rosen steering with qubit measurements

We demonstrate how quantum optimal control can be used to enhance quantum resources for bipartite one-way protocols, specifically Einstein-Podolsky-Rosen 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 optimization, 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 characterized 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 by using these monotones. We demonstrate resource control numerically by 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 the way to practical use of the rather abstract quantum resource theories