Untitled ItPeer review Critical Assessment and Referee-Style Review of Random Purification Channel for Arbitrary Symmetries with Applications to Fermions and Bosons - Michael Walter Freek Witteveenem

The manuscript introduces a symmetry-compatible random purification channel and applies it to fermionic andbosonic systems. The construction is mathematically well defined and technically correct.However, the manuscript implicitly assumes that the proposed channel is physically distinguished. This assumptionis not supported by either a variational principle or a uniqueness argument. As shown below, the stated constraintsadmit infinitely many inequivalent purification channels.