Abstract

The recently introduced random purification channel, which converts n i.i.d. copies of any mixed quantum state into a uniform convex combination of n i.i.d. copies of its purifications, has proved to be an extremely useful tool in quantum learning theory. Here we give a remarkably simple construction of this channel, making its known properties -- and several new ones -- immediately transparent. In particular, we show that the channel also purifies non-i.i.d. states: it transforms any permutationally symmetric state into a uniform convex combination of permutationally symmetric purifications, each differing only by a tensor-product unitary acting on the purifying system. We then apply the channel to give a one-line proof of (a stronger version of) the recently established Uhlmann's theorem for quantum divergences.

Personal information

Filippo graduated in Physics from the University of Pisa and the Scuola Normale Superiore. His master's thesis, supervised by Giacomo De Palma, focused on the characterization of quantum neural networks in the large-width limit. He then began his PhD at the University of Amsterdam and QuSoft under the supervision of Ludovico Lami. Following his advisor, he later moved to Pisa, where he is continuing his doctoral studies at the Scuola Normale Superiore. His current research focuses on quantum Shannon theory, especially hypothesis testing and communication, with recent interests in quantum learning theory and continuous-variable systems.

Reference

https://arxiv.org/abs/2511.23451