In most studies of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent investigations of the effect of memory or correlations in error have led to speculation that nonanalytic behavior may occur in the capacity. Motivated by these observations, we connect the study of channels with correlated error to the study of many-body systems. This enables us to use many-body theory to solve some interesting models of correlated error. These models can display nonanalyticities analogous to quantum phase transitions.

• Received 20 April 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.120504