  We address the swapping of various quantum correlation measures including:
Bell-nonlocality, EPR-steering, usefulness for teleportation, entanglement,
quantum obesity, as well as the effect that local filtering operations have on
the swapping of such correlations. In the first part of this work we address
the raw swapping protocol (i. e. without local filtering) and our findings are
as follows. First, using the Bloch representation of quantum states, we show
that all of the above properties of a general quantum state can fully be
preserved whenever the state is swapped together with arbitrary combinations of
Bell states and Bell measurements. This generalises a result shown for the
concurrence of states in the X-form. Second, we derive an explicit formula for
the quantum obesity of the final post-swapping state in terms of the obesity of
general input states and measurements, and therefore establishing the limit at
which obesity can be swapped. In the second part we address the effect of local
filtering operations on the swapping of quantum correlations. Specifically, we
explore whether experimentalists should implement local filters before or after
the swapping protocol takes place, so in order to maximize the final amount of
correlations. In this regard, we first show that these two scenarios are
equivalent for the family of Bell-diagonal states, for all of the
above-mentioned quantum correlations. We then prove that applying local filters
first can be more efficient when considering the strictly larger family of
almost Bell-diagonal states, with the quantum obesity as the test property.
Finally, we provide numerical evidence for this latter phenomenon (local
filtering first is more efficient) holding true for general two-qubit states in
the X-form, for all of the above-mentioned quantum correlations.
