  In terms of the characteristic functions of the quantum states, we present a
complete operator description of a lossy photon-subtraction scheme. Feeding a
single-mode squeezed vacuum into a variable beam splitter and counting the
photons in one of the output channels, a broad class of multiphoton-subtracted
squeezed vacuum states (MSSVSs) can be generated in other channel. Here the
losses are considered in the beginning and the end channels in the circuit.
Indeed, this scheme has been discussed in Ref. [Phys. Rev. A 100, 022341
(2019)]. However, different from the above work, we give all the details of the
optical fields in all stages. In addition, we present the analytical
expressions and numerical simulations for the success probability, the
quadrature squeezing effect, photon-number distribution and Wigner function of
the MSSVSs. Some interesting results effected by the losses are obtained.
