Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos

Understand

We develop a theory of symmetry in open quantum systems.

• Using the operator-state mapping, we characterize symmetry of Liouvillian superoperators for the open quantum dynamics by symmetry of operators in the double Hilbert space and apply the 38-fold internal-symmetry classification of non-Hermitian operators.
• We find rich symmetry classification due to the interplay between symmetry in the corresponding closed quantum systems and symmetry inherent in the construction of the Liouvillian superoperators.
• As an illustrative example of open quantum bosonic systems, we study symmetry classes of dissipative quantum spin models.