  Quantum (Poincar\'e) recurrence theorem are known for closed quantum
(classical) systems. Can recurrence happen in open systems? We provide the
recurrence theorem for open quantum systems via non-Hermitian (NH) description.
We find that PT symmetry and pseudo-Hermitian symmetry protect recurrence for
NH open quantum systems and the recurrence fails with the symmetry breaking.
  Applying our theorem to PT-symmetric systems, we reveal why quantum
recurrence happens in PT-unbroken phase but fails in PT-broken phase, which was
misunderstood before.
  A contradiction emerges when we apply our theorem to anti-PT symmetric
systems and we settle it, revealing that distinguishability and von Neumann
entropy are generally not effective to describe the information dynamics in NH
systems.
  A new approach is developed to investigate the information dynamics of NH
systems. For anti-PT symmetric systems in PT-broken phase, we find there are
three information-dynamics patterns: oscillations with an overall decrease
(increase) , and periodic oscillations. The periodic oscillations (information
complete retrieval) happen only if the spectrum of NH Hamiltonian is real. The
three patterns degenerate to the periodic oscillation using distinguishability
or von Neumann entropy because normalization of non-unitary evolved states
leads to loss of information. We conclude with a discussion of the physical
meaning behind the recurrence in open systems and give the direction of
recurrence theorem not limited to conservative systems in classical mechanics.
