  Subtracting photons from a two-mode squeezed state is a well-known method to
increase entanglement. We analyse different strategies of local photon
subtraction from a two-mode squeezed state in terms of entanglement gain and
success probability. We develop a general framework that incorporates
imperfections and losses in all stages of the process: before, during, and
after subtraction. By combining all three effects into a single efficiency
parameter, we provide analytical and numerical results for subtraction
strategies using photon-number-resolving and threshold detectors. We compare
the entanglement gain afforded by symmetric and asymmetric subtraction
scenarios across the two modes. For a given amount of loss, we identify an
optimised set of parameters, such as initial squeezing and subtraction beam
splitter transmissivity, that maximise the entanglement gain rate. We identify
regimes for which asymmetric subtraction of different Fock states on the two
modes outperforms symmetric strategies. In the lossless limit, subtracting a
single photon from one mode always produces the highest entanglement gain rate.
In the lossy case, the optimal strategy depends strongly on the losses on each
mode individually, such that there is no general optimal strategy. Rather,
taking losses on each mode as the only input parameters, we can identify the
optimal subtraction strategy and required beam splitter transmissivities and
initial squeezing parameter. Finally, we discuss the implications of our
results for the distillation of continuous-variable quantum entanglement.
