  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
