  To easily calculate statistical properties of pairs correlated through
Schmidt decomposition, as commonly used in Quantum Information, we propose a
"commutator formalism" for these single-index pairs, somewhat simpler than the
one we developed for double-index Wannier excitons. We use it here to get the
pair number threshold for bosonic behavior of $N$ pairs through the requirement
that their number operator mean value must stay close to $N$. While the main
term of this mean value is controlled by the second moment of the Schmidt
distribution, so that to increase this threshold, we must increase the Schmidt
number, higher momenta appearing at higher orders lead to choosing a
distribution as flat as possible.
