The main issues in quantum detection theory are the injectivity and state estimation problems, which recently linked and partially studied via frame theory on Hilbert spaces. Inspired by some recent researches and works on the quantum detection problem by (discrete) frames, continuous frames and fusion frames, in this note we examine the quantum detection problem for generalized frames (g-frames). In the theory of g-frames, instead of using the frame element itself, we use a family of bounded operators.We characterize injectivity problem by g-frames and with the help of these characterizations, we give some equivalent conditions for the injectivity problems. We answer the injectivity problems both for trace and Hilbert-Schmidt classes of operators.
