  From the perspective of majorization theory, we study how to enhance the
entanglement of a two-mode squeezed vacuum (TMSV) state by using local
filtration operations. We present several schemes achieving entanglement
enhancement with photon addition and subtraction, and then consider filtration
as a general probabilistic procedure consisting in acting with local
(non-unitary) operators on each mode. From this, we identify a sufficient set
of two conditions on filtration operators for successfully enhancing the
entanglement of a TMSV state, namely the operators must be Fock-orthogonal
(i.e., preserving the orthogonality of Fock states) and Fock-amplifying (i.e.,
giving larger amplitudes to larger Fock states). Our results notably prove that
ideal photon addition, subtraction, and any concatenation thereof always
enhance the entanglement of a TMSV state in the sense of majorization theory.
We further investigate the case of realistic photon addition (subtraction) and
are able to upper bound the distance between a realistic photon-added
(-subtracted) TMSV state and a nearby state that is provably more entangled
than the TMSV, thus extending entanglement enhancement to practical schemes via
the use of a notion of approximate majorization. Finally, we consider the state
resulting from $k$-photon addition (on each of the two modes) on a TMSV state.
We prove analytically that the state corresponding to $k=1$ majorizes any state
corresponding to $2\leq k \leq 8$ and we conjecture the validity of the
statement for all $k\geq 9$.
