Strong symmetries in collision models and physical dilations of covariant quantum maps

Strong symmetries in collision models and physical dilations of covariant quantum maps

Seminar author:Marco Cattaneo

Event date and time:10/30/2025 11:30:am

Event location:Seminars Room,GIQ

Event contact:

Quantum maps are fundamental to quantum information theory and open quantum systems. Covariant or weakly symmetric quantum maps, in particular, play a key role in defining quantum evolutions that respect thermodynamics, establish free operations in resource theories, and are consistent with transformations of quantum reference frames. To implement quantum maps in the laboratory, one typically engineers a physical dilation, which corresponds to a unitary evolution entangling the system with an environment. In the talk, we systematically explore how weak symmetries of quantum maps manifest in their dilations. We demonstrate that for various classes of physical dilations, including Hamiltonian-driven dilations and short-time collision models that simulate Markovian open quantum dynamics, weak symmetries always lead to strong symmetries in the dilated evolution, resulting in conserved quantities in the system-environment space. We also characterize the subspace where these symmetries arise using Krylov subspaces. Moreover, we show that some different types of physical dilations have no constraints on the dilated evolution, requiring no strong symmetry. Finally, we provide some examples by applying our findings to single-qubit Pauli channels, such as phase damping and depolarizing channels.