| Description |
The theory of open quantum systems is the backbone of Quantum Information science. It is impossible to isolate a particular quantum system from its environment and it is subjected to information loss in the form of decoherence. In modelling open quantum systems, the simpler approach is to consider the environment to be Markovian. The system-environment relation is, however, more often than not, non-Markovian, and there are possibilities of information back flow into the system, which can be considered as a resource in information theoretic tasks. On the other hand, an important statistical mechanical attribute of a system interacting with an environment, with the later being in a thermal state, is the ergodicity of the system. We establish uncertainty relations between information loss in general open quantum systems and the amount of nonergodicity of the corresponding dynamics. The relations hold for arbitrary quantum systems interacting with an arbitrary quantum environment. The relations show that as the nonergodicity of the dynamics increases, the lower bound on information loss decreases, which validates the belief that nonergodicity plays an important role in preserving information of quantum states undergoing lossy evolution.
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