  The notion of entanglement of quantum states is usually defined with respect
to a fixed bipartition. Indeed, a global basis change can always map an
entangled state to a separable one. The situation is however different when
considering a set of states. In this work we define the notion of an
"absolutely entangled set" of quantum states: for any possible choice of global
basis, at least one of the states in the set is entangled. Hence, for all
bipartitions, i.e. any possible definition of the subsystems, the set features
entanglement. We present a minimum example of this phenomenon, with a set of
four states in $\mathbb{C}^4 = \mathbb{C}^2 \otimes \mathbb{C}^2$. Moreover, we
propose a quantitative measure for absolute set entanglement. To lower-bound
this quantity, we develop a method based on polynomial optimization to perform
convex optimization over unitaries, which is of independent interest.
