Spectral Properties of Symmetry-Constrained Quantum Channels

Abstract

Studying the spectral properties of symmetric quantum channels allows us to characterize the dynamics of open quantum systems constrained by conservation laws. In this thesis, we investigate the spectral properties of quantum channels with U(1) symmetry, with emphasis on the strongly U(1)-symmetric case. Specifically, we focus on translationally invariant Floquet circuits that are subject to depolarizing noise (weakly symmetric case) and dephasing noise (strongly symmetric case). Each channel is constructed as a Liouville superoperator, and we perform a spectral decomposition to analyze its eigenvalue spectrum. For the strongly U(1)-symmetric channel, we exploit the block-diagonal structure of the superoperator across the U(1) charge sectors and characterize its symmetry-resolved spectrum. Numerical results reveal a unique steady state within each sector, corresponding to the maximally mixed state within the sector. Furthermore, we analyze the many-body weight distributions of the leading eigenmodes and find that the slow modes are dominated by components with low effective Pauli weights, as high-weight components decay faster under dephasing noise.