Invariance in multi-objective quantum control

Simultaneous optimization of multiple quantum objectives is often considered a demanding task. However, a special circumstance arises when a primary objective is pitted against a set of secondary objectives, which we show leads to invariant behavior of the secondary objectives upon the primary one approaching its optimal value. Still, practical relationships among the objectives will generally lead to a threshold, beyond which system re-engineering is required to further increase the primary objective. This finding is of broad significance for reaching high performance in quantum technologies