Fate of symmetry protected coherence in open quantum system

We investigate the fate of coherence in dynamical evolution symmetry protected quantum systems. Under formalism system plus bath for open systems, antiunitary symmetries exhibit significant differences from unitary ones protecting initial coherence. Specifically, taking advantage Lindblad master equation, we find that a pure state degenerate subspace will be decoherent even though both Hamiltonian and system-environment interaction respect same symmetry. In contrast, persist when is unitary. provide an elaborate classification table to illustrate what kinds combinations are able preserve state, which confirmed several concrete models single spin-$3/2$ It can also applied Haldane phase interacting topological Our results could helpful exploring possible experimental realization stable time-reversal symmetric states.