  We develop a theoretical framework for the dissipative propagation of
quantized light in interacting optical media under conditions of
electromagnetically induced transparency (EIT). The theory allows us to
determine the peculiar spatiotemporal structure of the output of two
complementary Rydberg-EIT-based light-processing modules: the recently
demonstrated single-photon filter and the recently proposed single-photon
subtractor, which, respectively, let through and absorb a single photon. In
addition to being crucial for applications of these and other optical quantum
devices, the theory opens the door to the study of exotic dissipative many-body
dynamics of strongly interacting photons in nonlinear nonlocal media.
