  A set of quantum states is said to be absolutely entangled, when at least one
state in the set remains entangled for any definition of subsystems, i.e. for
any choice of the global reference frame. In this work we investigate the
properties of absolutey entangled sets (AES) of pure quantum states. For the
case of a two-qubit system, we present a sufficient condition to detect an AES,
and use it to construct families of $N$ states such that $N-3$ (the maximal
possible number) remain entangled for any definition of subsystems. For a
general bipartition $d=d_1d_2$, we prove that sets of
$N>\left\lfloor{(d_{1}+1)(d_{2}+1)/2}\right \rfloor$ states are AES with Haar
measure 1. Then, we define AES for multipartitions. We derive a general lower
bound on the number of states in an AES for a given multipartition, and also
construct explicit examples. In particular, we exhibit an AES with respect to
any possible multi-partitioning of the total system.
