  Loss induced generalized measurements have been introduced years ago as a
mean to implement generalized quantum measurements (POVM). Here the original
idea is extended to a complete equivalence of lossy evolution and a certain
widely used class of POVM. This class includes POVM used for unambiguous state
discrimination and entanglement concentration. One implication of this
equivalence is that unambiguous state discrimination schemes based on
PT-symmetric and non-Hermitian Hamiltonians have the same performance as those
of standard POVM. After discussing several key points of this equivalence we
illustrate our findings in two elementary physical realizations. Finally, we
discuss several implications of this equivalence.
