  There is a debate in course about the quantification of entanglement of
indistinguishable particles and recently a new method due to Lo Franco and
Compagno (LFC) [Sci. Rep. \textbf{6}, 20603 (2016)] appeared with the aim of
settling the controversies of this debate. In this work we show that the LFC
approach can be recovered using the second quantization formalism and a local
single-particle basis to perform the trace over one particle state. The use of
the second quantization formalism has the advantage of being well known in
many-body physics. We also compare the LFC and second quantization approaches,
or equivalently, the effect of the partial trace over one particle depending on
the local and nonlocal caracter of the single-particle basis. Additionally, we
study the role played by the exchange correlations in the quantification of
entanglement of indistinguishable particles.
