  The conventional photon subtraction and photon addition transformations,
$\varrho \rightarrow t a \varrho a^{\dag}$ and $\varrho \rightarrow t a^{\dag}
\varrho a$, are not valid quantum operations for any constant $t>0$ since these
transformations are not trace nonincreasing. For a fixed density operator
$\varrho$ there exist fair quantum operations, ${\cal N}_{-}$ and ${\cal
N}_{+}$, whose conditional output states approximate the normalized outputs of
former transformations with an arbitrary accuracy. However, the uniform
convergence for some classes of density operators $\varrho$ has remained
essentially unknown. Here we show that, in the case of photon addition
operation, the uniform convergence takes place for the
energy-second-moment-constrained states such that ${\rm tr}[\varrho H^2] \leq
E_2 < \infty$, $H = a^{\dag}a$. In the case of photon subtraction, the uniform
convergence takes place for the energy-second-moment-constrained states with
nonvanishing energy, i.e., the states $\varrho$ such that ${\rm tr}[\varrho H]
\geq E_1 >0$ and ${\rm tr}[\varrho H^2] \leq E_2 < \infty$. We prove that these
conditions cannot be relaxed and generalize the results to the cases of
multiple photon subtraction and addition.
