  We study the capacity of a quantum channel where channel acts like controlled
phase gate with the control being provided by a one-dimensional quantum spin
chain environment. Due to the correlations in the spin chain, we get a quantum
channel with memory. We derive formulas for the quantum capacity of this
channel when the spin state is a matrix product state. Particularly, we derive
exact formulas for the capacity of the quantum memory channel when the
environment state is the ground state of the AKLT model and the Majumdar-Ghosh
model. We find that the behavior of the capacity for the range of the
parameters is analytic.
