Self-restricting Noise and Quantum Relative Entropy Decay
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Open quantum systems as modeled by quantum channels and quantum Markov semigroups usually decay to subspaces that are invariant under environmental interactions. It is known that finite-dimensional semigroups with detailed balance decay exponentially under modified logarithmic-Sobolev inequalities (MLSIs). Here we analyze discrete and continuous processes that include unitary components, breaking the detailed balance assumption. We find counter-examples to analogs of MLSIs for these systems. The generalized quantum Zeno effect appears for many Lindbladians that combine a decay process with unitary drift. As incompatible long-time and Zeno limits compete, strong noise often protects subsystems and subspaces from its own spread. We observe this interplay between decay and Zeno-like effects experimentally on superconducting qubits using IBM Q devices. Nonetheless, by combining MLSIs for effective self-adjoint decay processes across different times, we obtain eventual exponential decay. We similarly obtain decay rate lower bounds for discrete compositions of quantum channels.
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