In many studies of channel capacities an independent error model is assumed. However, in reality the environment will usually have a `memory' that leads to correlations in the errors affecting successive transmissions. Despite their physical importance, `memory channels' are exceedingly hard to analyze, and their communication capacities are rarely known. On the other hand correlations are a key concern in the seemingly unrelated area of statistical physics, and its key branch of interacting many-body systems. Here we provide a natural connection between the study of quantum memory channels and the study of the statistical mechanics of interacting many body systems. This connection enables us to develop non-trivial `exactly solvable' models of memory channels that can display similar behaviour to many-body systems, including manifestations of `phase transitions'.
展开▼
