Universal purification dynamics in real non-unitary quantum processes
Abstract
We study purification dynamics in monitored quantum processes governed by ensembles of quantum circuits in different random-matrix symmetry classes. We analyze the universal aspects that emerge away from the measurement-induced phase transition and inside the volume/weak measurement phase and in the scaling limit of large time and Hilbert space dimension. We present two toy models that reveal two complementary visions and provide quantitative access to universal scaling: (i) a discrete-time dynamic in which each time step corresponds to multiplication by a Gaussian random matrix; (ii) weak continuous-time monitoring that induces a Dyson Brownian motion of the eigenvalues of the density matrix. The first approach provides an algebraic characterization based on rotational invariance emerging in Kraus's operator space, focusing in particular on the unitary and orthogonal cases, respectively β = 2 and β = 1, with β the Dyson random-matrix index. The second approach, on the other hand, allows for a unified treatment for any β, thanks to the mapping of the Fokker-Planck evolution of eigenvalues onto the Calogero-Sutherland integrable Hamiltonian diagonalized in terms of Jack polynomials. We provide explicit expressions for the universal decrease of Rényi entropies. We show that, approaching the universal scaling limit, numerical simulations of different models agree with each other and with our theoretical predictions. Our results clarify the existence of different classes of universality for the purification process in hybrid quantum systems, accessible in random circuit architectures and weak measurement protocols.
Related
- Universal purification dynamics of monitored Clifford circuits
- Probabilistic and approximate universal quantum purification machines
- Universal Entanglement Dynamics of Unitary Operators
- A Compilation Framework for Quantum Simulation of Non-unitary Dynamics
- A unifying framework for quantum algorithms for time-dependent non-unitary dynamics
BibTeX
@article{gerbino2026universal,
title = {{Universal purification dynamics in real non-unitary quantum processes}},
author = {Federico Gerbino and Donghoon Kim and Guido Giachetti and Andrea De Luca and Xhek Turkeshi},
journal = {Reports on Progress in Physics},
year = {2026},
month = sep,
doi = {10.1088/1361-6633/aea249},
eprint = {2603.10751},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05769185v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Universal purification dynamics in real non-unitary quantum processes
AU - Federico Gerbino
AU - Donghoon Kim
AU - Guido Giachetti
AU - Andrea De Luca
AU - Xhek Turkeshi
PY - 2026
DA - 2026/09/17
JO - Reports on Progress in Physics
DO - 10.1088/1361-6633/aea249
UR - https://hal.science/hal-05769185v1
AB - We study purification dynamics in monitored quantum processes governed by ensembles of quantum circuits in different random-matrix symmetry classes. We analyze the universal aspects that emerge away from the measurement-induced phase transition and inside the volume/weak measurement phase and in the scaling limit of large time and Hilbert space dimension. We present two toy models that reveal two complementary visions and provide quantitative access to universal scaling: (i) a discrete-time dynamic in which each time step corresponds to multiplication by a Gaussian random matrix; (ii) weak continuous-time monitoring that induces a Dyson Brownian motion of the eigenvalues of the density matrix. The first approach provides an algebraic characterization based on rotational invariance emerging in Kraus's operator space, focusing in particular on the unitary and orthogonal cases, respectively β = 2 and β = 1, with β the Dyson random-matrix index. The second approach, on the other hand, allows for a unified treatment for any β, thanks to the mapping of the Fokker-Planck evolution of eigenvalues onto the Calogero-Sutherland integrable Hamiltonian diagonalized in terms of Jack polynomials. We provide explicit expressions for the universal decrease of Rényi entropies. We show that, approaching the universal scaling limit, numerical simulations of different models agree with each other and with our theoretical predictions. Our results clarify the existence of different classes of universality for the purification process in hybrid quantum systems, accessible in random circuit architectures and weak measurement protocols.
SN - 0034-4885
SN - 1361-6633
ER -