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Driven-dissipative quantum systems generically do not satisfy simple notionsof detailed balance based on the time symmetry of correlation functions. Weshow that such systems can nonetheless exhibit a hidden time-reversal symmetrywhich most directly manifests itself in a doubled version of the originalsystem prepared in an appropriate entangled thermofield double state. Thishidden time-reversal symmetry has a direct operational utility: it provides ageneral method for finding exact solutions of non-trivial steady states.Special cases of this approach include the coherent quantum absorber andcomplex-$P$ function methods from quantum optics. We also show that hidden TRShas observable consequences even in single-system experiments, and can bebroken by the non-trivial combination of nonlinearity, thermal fluctuations,and driving. To illustrate our ideas, we analyze concrete examples of drivenqubits and nonlinear cavities. These systems exhibit hidden time-reversalsymmetry but not conventional detailed balance.

Hidden time-reversal symmetry, quantum detailed balance and exact solutions of driven-dissipative quantum systems