  Quantum resource theories offer a powerful framework for studying various
phenomena in quantum physics. Despite considerable effort has been devoted to
developing a unified framework of resource theories, there are few common
properties that hold for all quantum resources. In this paper, we fill this gap
by introducing the flag additivity based on the tensor product structure and
the flag basis for the general quantum resources. To illustrate the usefulness
of flag additivity, we show that flag additivity can be used to derive other
nontrivial properties in quantum resource theories, e.g., strong monotonicity,
convexity, and full additivity.
