Author(s): Lauritz van Luijk, Alexander Stottmeister, and Henrik Wilming The uniqueness of purifications of quantum states on a system A up to local unitary transformations on a purifying system B is central to quantum information theory. We show that, if the two systems are modeled by commuting von Neumann algebras M A and M B on a Hilbert space H , then uniqueness of puri… [Phys. Rev. Lett. 136, 040203] Published Fri Jan 30, 2026