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In most studies of the capacity of quantum channels, it is assumed that theerrors in each use of the channel are independent. However, recent work hasbegun to investigate the effects of memory or correlations in the error, andhas led to suggestions that there can be interesting non-analytic behaviour inthe capacity of such channels. In a previous paper we pursued this issue byconnecting the study of channel capacities under correlated error to the studyof critical behaviour in many-body physics. This connection enables the use oftechniques from many-body physics to either completely solve or understandqualitatively a number of interesting models of correlated error with analogousbehaviour to associated many-body systems. However, in order for this approachto work rigorously, there are a number of technical properties that need to beestablished for the lattice systems being considered. In this article wediscuss these properties in detail, and establish them for some classes ofmany-body system.

Many body physics and the capacity of quantum channels with memory