Random purification channel for passive Gaussian bosons

Francesco Anna Mele, Filippo Girardi, Senrui Chen, Marco Fanizza, Ludovico Lami (Dec 19 2025).

Abstract: The random purification channel, which, given $n$ copies of an unknown mixed state $\rho$, prepares $n$ copies of an associated random purification, has proved to be an extremely valuable tool in quantum information theory. In this work, we construct a Gaussian version of this channel that, given $n$ copies of a bosonic passive Gaussian state, prepares $n$ copies of one of its randomly chosen Gaussian purifications. The construction has the additional advantage that each purification has a mean photon number which is exactly twice that of the initial state. Our construction relies on the characterisation of the commutant of passive Gaussian unitaries via the representation theory of dual reductive pairs of unitary groups.

Arxiv: https://arxiv.org/abs/2512.16878