Compressing compound states

Quantum compression can be thought of not only as compression of a signal, but also as a form of cooling. In this view, one is interested not in the signal, but in obtaining purity. In compound systems, one may be interested to cool the system to obtain {\it local purity} by use of local operations and classical communication [Oppenheim et al. Phys. Rev. Lett. 89,180402 (2002)]. Here we compare it with usual compression and find that it can be represented as compression with suitably restricted means.